The below is a list of easter eggs which can be found in the Halo 3 campaign, listed in mission order. Viewing some of these may unlock achievements and if that's the case, I'll note as such.

Table of contents:

Mission names are underlined
Easter egg names are in bold

Sierra 117 *
MF Tree Carving
M + L 7-16-95 Tree Carving
Caveman in tree *
Caveman family *
Sam + Grady ♥ Dad Tree Carving
Lone Caveman *

Crow's Nest
Red Vs Blue/Rooster Teeth Voices

The Storm
Boat that looks like Mark VI helmet
Pirate Poster

Floodgate *
Missing person poster *

The Ark
Urinating Brute

The Covenant *
Siege of Madrigal *
Microsoft Sam
Secret Marines

Halo *
Floating man in Underwear *
Hidden Talking Grunt *

⠀
MF Tree Carving

A tree carving can be found near the beginning of the level, in the shaded area full of grunts after exiting the first cave.
⠀
⠀
Follow the area to the back on the left-hand side, until you reach this area:
⠀
⠀
You'll notice a tree with two branches sticking out to the left and right. You'll want to jump on the branch sticking out to the left.
⠀
⠀
When on this branch, turn right and jump onto the one I'm aiming at below.
⠀
⠀
Turn left once you've landed, and jump up to the branch below.
⠀
⠀
Looking at the connecting branch, you can find the carving. It's easiest viewed with the flashlight turned on.
⠀
⠀
M + L 7-16-95 Tree Carving

In the immediate area following on from the previous tree carving, you'll find a Brute holding a UNSC marine by the neck. If you follow the area around and up to bridge the brute and marine were on, instead jump into the tree highlighted below and look at the branch to the left to find the carving.
⠀
⠀
Caveman in tree *

This lone caveman can be found overlooking the area next to the river where the Pelican is shot down.
⠀
⠀
Look out over the water into the treeline at the back and the caveman can be found between the fork of these two branches.
⠀
⠀
It can be very difficult to see even with a ranged weapon, but looking at him (or shooting which is what I did) will unlock the achievement Missing Link
⠀
Caveman family *

The caveman family can be seen after entering the Charlie Foxtrot portion of the level.

Fight past the area where the pelican is shot down by the river from the previous egg
and make your way through to the next area under the leaky pipe, where the Jackal snipers are located. Keep following straight until you get to a point where you have to turn right round a corner to continue; on your left, there will be an outcropping that looks like this:
⠀
⠀
Walk across this ledge until you get to the end then look left and you'll find the bizarre little family.
⠀
⠀
Viewing the cavemen will unlock the achievement Primal. (It didn't unlock until I zoomed in)
⠀
Sam + Grady ♥ Dad Tree Carving

The final tree carving can be found in the same area as the caveman family. Standing where the family are, turn around and face back the way you came. you'll want to get on top of the rock highlighted here:
⠀
⠀
Walk along the rock and there'll be a tree with a low-hanging branch you can drop down onto.
⠀
⠀
Once on this branch, turn to look at the trunk of the tree and you'll see the carving.
⠀
⠀
Lone Caveman *

A single caveman can be found off in the distance right at the very end of the level. When you get to the Dam section where you have to rescue Johnson, stand on the platform highlighted below and look up into the cliffs above -- you can just about make out the lone caveman overlooking the Dam. Best viewed with a scoped weapon.

Viewing this caveman will unlock the achievement Haplorhini
⠀

⠀
Red Vs Blue/Rooster Teeth Voices

Another of the most famous easter eggs in the game, this one can be found near the beginning of the level. You'll enter a corridor and see a few marines in a warthog get blown up by a plasma grenade.
Fight your way through all of the Covenant in this corridor, but continue past the door you're supposed to proceed through and follow it all the way to the end.

Here you'll find a marine, voiced by a member of Rooster Teeth, talking to another marine through a door, also voiced by a member of Rooster Teeth.

The voices change depending on the difficulty you're playing.
⠀

⠀
Boat that looks like Mark VI helmet

When you get to the second outdoor area where you fight the scarab, you'll see there's a large abandoned boat close to where you enter the area. If viewed from rear, it looks very similar to a certain someone's helmet.
⠀
⠀
Pirate Poster

You'll want to use the Acrophobia skull for this one.

Float up to the top of the boat from the area where you fight the scarab and there'll be a couple of holes you can use to enter a small room at the top of the boat. On the wall in this room is a poster with a man in a pirate hat and the words "sheik of the sea" written below.

This is apparently a reference to Bungie employee Shi Kai Wang.
⠀

⠀
Missing person poster *

Right at the beginning of the mission, you'll re-enter the industrial area from the end of the previous level. Directly in front as soon as you enter is a fence gate with fire behind it. Turn left to continue on with the level and you'll see some garage-looking structures to the left and right. The poster can be found on the first of these on the right. It's on the floor at the back.

It's a poster of Jason Jones, one of Bungie's co-founders.

Looking at this poster unlocks the achievement Milk Carton
⠀

⠀
Urinating Brute

This brute can be found in the far-right corner of the room with the sleeping grunts, after the scarab fight. You enter this room just after 343 Guilty Spark shocks the Marine. You start directly here from rally point Charlie.
⠀

⠀
Siege of Madrigal *

The hidden music track can be found in the area where you fight the two scarabs, directly before entering the citadel. Once the scarabs have been destroyed and all enemies taken out, you'll want to take a hornet up to the left side of the citadel and land it on the ledge highlighted below.
⠀
⠀
Once you've landed it, follow the ledge to the back of the structure, then walk up the incline to the very top. Once you've reached the top, the music should begin playing more or less immediately.
⠀
⠀
Listening to the music track unlocks the achievement Dirge of Madrigal
⠀
Microsoft Sam

On the opposite side of the structure to the above, waiting in the same spot will eventually trigger some dialogue voiced by the Microsoft Sam Windows speech synthesis program.

This can only be heard on normal difficulty and above, and the mission must be played from the very beginning.


⠀
Secret Marines

Try as I might, I could not get this to work in the Master Chief Collection as of 20/07/2024 - but I do remember this being possible in the Xbox 360 version of the game back in the day - unfortunately, for this reason I won't be able to provide any screenshots myself.

Further information on the secret marines can be found here: https://www.halopedia.org/Secret_Marine_on_The_Covenant

⠀
Floating man in Underwear *

From the beginning of the mission, head forwards and through the cave up to the point where you need to drop down the point of no return. Instead, turn right and head into the corridor which leads to the final terminal.
⠀
⠀
Instead of heading left to the terminal however, you'll want to head right and continue forward into the tunnel - keep moving forward until you reach the abyss with a metallic platform off in the distance. You need to get to this platform, either with a good grenade jump, using a friend to double-jump or better yet, use the Acrophobia skull with trivialises this easter egg.
⠀
⠀
Now you're on this platform, look to the left and there'll be an alcove you can hop onto. Do so, then carry on walking to the end, where you'll find Jason Jones floating in his underwear.
⠀
⠀
Viewing Jason here unlocks the achievement Heading to his Destiny

Hidden Talking Grunt *

Right at the very end of the mission during the warthog run, just before you drive down the ramp to jump into the Forward Unto Dawn you'll pass under a rock-arch formation. You'll want to head right around the right-side of the rock and here you'll find the Grunt. If you approach him, he'll have some interesting stuff to say to you.
⠀
⠀
Listening to the grunt talk ♥♥♥♥ will unlock the achievement Cool Story Bro

Below is a list of easter eggs available to find within the multiplayer maps. Maps listed alphabetically.

Table of contents:

Map names are underlined
Easter egg names are in bold

Assembly *
Assembly skull *

Construct
Marathon logo

Foundry *
UNSC Draft Notice
"It Glows" Football Poster
Trash Hippo *

High Ground *
Cortana Image
Halo Music *

Isolation
Spreading Flood growth

Last Resort
Flexing Cloud

Longshore
Suck it Fronk
Fish Taco Hut Menu
Fronk the whale opening his eyes
Dead rats

Orbital *
Lorem Ipsum
Covenant on Earth!
Orbital Skull *

Sandtrap
Half-life reference
Elephant flip message

Snowbound
Canadian Coin

Standoff *
Man on the moon *
Satellite Dish Man
"HOWL"
If you can read this, you're too close

The Pit
Halo 3 Logo
Microsoft Windows Logo

Valhalla *
Valhalla Wall Messages *

⠀
Assembly Skull *

Go to the segment of the map with the 3 short cylinders and look at the central map structure. To the left of this structure will be a pipe bending up and away from it. The skull is located where the pipe connects to the structure.

The easiest way to pick the skull up is to load the map in Forge and drop onto the pipe from above in edit mode.

⠀
Picking up the Assembly Skull will unlock the achievement Assembly Skull

⠀
Marathon logo

There is a pit in the ceiling of the bottom level of the map, which when peered into from the right angle, from above, will show the logo of the Marathon games, which Bungie worked on before Halo.

⠀

In many of the empty piles of trash dotted throughout the map, you can find discarded UNSC draft notices.
⠀
⠀

Behind the fencing which lines the walls of the corridor which can be found at the back of the left-side of the map, Corridor 02, is a poster showing an image of a football (or soccer ball, depending where you're from), with the text "It Glows" written beneath.

It can be viewed through the fencing, but is more easily seen by using the turret glitch in Forge to get behind the fence.
⠀
⠀

In a pile of trash on the map, you can find the front half of a Hippopotamus toy smiling up at you.

Viewing this Hippo for long enough will unlock the achievement Hippo Hero (Thanks to Zacklego for updating me on this one)
⠀

⠀
Cortana Image

In the base area of the map, there is a small room with a broken wall in which you'll find a couple of computers and a radio. If you enter through the break in the wall and turn left, there'll be a computer with several displays resting on a table next to a radio.

This computer has what appears to be a live video feed of some sort of hangar. If you watch this feed, after a short while a fairly creepy looking image of Cortana will briefly flash up before going back to normal. This repeats around every two or so minutes.
⠀
⠀
Halo Music *

In the same room as the Cortana Computer but located on the opposite wall, you can find another computer on a table, this time with a radio beneath. You'll notice this radio is playing static and morse code. If you stick around in this room near the radio, eventually it'll make a noise as though it is tuning into a radio station and will then play a random track from one of the Halo games.

Waiting for the radio to play one of these songs on this map will grant you the achievement Sounds Familiar
⠀

⠀
Spreading Flood growth

Over the course of a match on this map, the grassy section above the central tunnel which leads to the Flood-infected interior of the map, will itself gradually become more and more pockmarked with Flood spores and growths.


(Image from https://www.halopedia.org/Isolation )

⠀
Flexing Cloud

If you go to the beach area and look out into the ocean, then look at the sky to right, you'll see a cloud that takes the shape of a UNSC marine showing off his sweet corps-issued guns.
⠀

⠀
Suck it Fronk

If you go to the section of the map where the Fish Tacos hut is found, then face the large building opposite, you'll notice that one of the doors is marked "Freezer"
Enter this door and look through the windows immediately ahead to find the barely-legible message "Suck it Fronk" written on the wall.
⠀
⠀
This message will change depending on the date of the year.
⠀

• Christmas Day: Seventh Column
  
• Bungie Day (July 7th): The sign reads "7/7/7"
  
• Halloween: A skull
  
• July 4: The sign reads "Home of The Free"
  
• Cinco De Mayo: The sign reads "Root Beer @ Bob's Place"
  
• New Years Day: The sign reads "Flash Freeze This" (Most likely a reference to the popular show Futurama when the main character is flash frozen on New Year's Day 2000)
  
• Earth Day: An image of Fronk is there with the words "Save me" above him and "Eat Beef" below him. This is possibly a reference to the popular Advice Dog images found throughout the internet, as two completely different and unrelated pieces of advice are listed above and below a dogs head
  
• Veterans Day: A Spartan hand giving a "rock on" gesture.

⠀
(Information taken from https://halo.fandom.com/wiki/Suck_it_Fronk )
⠀
Fish Taco Hut Menu

Similarly to the above Easter Egg, if you head to the Tacos Hut you'll see there's menu outside and inside; this menu will change depending on the day of the year, such as Halloween and New Years.

Default menu:
⠀

• Monday: Fish Tacos
  
• Tuesday: Fish Tacos
  
• Wednesday: Fish Tacos
  
• Thursday: Fish Tacos
  
• Friday: Pie

Halloween:

• Monday: Fish brain
  
• Tuesday: Cod milt
  
• Wednesday: Egg sacks
  
• Thursday: Fish eyes
  
• Friday: Barry breaded balls

New Year:

• Monday: Salmon gyros
  
• Tuesday: Salmon gyros
  
• Wednesday: Tuna gyros
  
• Thursday: Whale gyros
  
• Friday: Dolphin gyro

(Halloween and New Year menu screenshots taken from https://www.halopedia.org/Longshore )
⠀
Fronk the whale opening his eyes

On the opposite end of the map to the fish taco hut, on top of the building where Red team spawn, you can find an image of Fronk the Whale on the side of where the stairs come up.
⠀
⠀
This image of Fronk starts with his eyes almost completely shut, but every 1m 45s will slightly open his eyes. This will continue for seven cycles until his eyes are fully open.

⠀
Dead rats
⠀
Rat 1

There are a couple of locations with some hard-to-see dead rats throughout the map - best found when playing in forge mode.

Firstly, you'll want to head back to the good old Fish Taco stand and head on inside, where you'll notice in the middle of the oven section there's a hollowed-out section (For a deep-fat fryer?)


If you switch to monitor mode whilst in forge, you can float up to get a good angle to view inside these recess, where you'll notice the first dead rat.

⠀
Rat 2

For our second rodent friend, exit the fish taco shack, get some air and then turn around so you're facing the shack. Now to you're right you'll see a couple of light poles with anti-bird spikes on the other end of the harbour - you'll want to make you're way to the left-most one next to the building, which I've highlighted below.


When you're close to the pole, make sure you get above it, and the part with the rat is the one which goes out in the direction of the water.

⠀
Lorem Ipsum

If you zoom in on many of the screens on this map, you can see that the text is actually "Lorem ipsum", a popular placeholer text used in design.

⠀
Covenant on Earth!

From the red spawn area, if you take the stairs up onto the catwalk and head over to the dark corner on the catwalk as highlighted in the image below, on the floor you can find a discarded newspaper with the headline "Covenent on Earth!"

⠀
Orbital Skull *

In the middle of the map is the area where the rocket spawns on a small ledge overhanging a death pit. High above this area, in the corner of a small alcover in the wall you can find the Orbital Skull, which you can pick up. This is most easily done in Forge mode by flying up to the skull in edit mode, then switching to play mode and holding the weapon pickup key to grab it as you fall.

⠀
Picking up the Orbital Skull will unlock the achievment Orbital Skull

⠀
Half-life reference

This may be an intentional reference or a happy coincidence, but for completion's sake I shall be including it, as many people believe this to be a direct reference.

If you go the temple with the underground section located at the far end of the map, within the underground section you can find a crowbar, Gordon Freeman's signature weapon from the Half-Life series. It should also be noted that the eighth chapter of Half-Life 2 is named "Sandtraps"
⠀

⠀
Elephant flip message

If you somehow manage to get a Elephant vehicle flipped over on this map, you can push a button to flip it over, like all other vehicles.

Given the Elephant's massive size and presumably enormous weight, the flip prompt will aptly note:
"Hold [button] to flip... wait, what? How did you do that?"

⠀
Canadian Coin

In the tunnel housing the active camo is a Canadian $1 coin. The coin can be found directly beneath the active camo pick-up.
⠀

⠀
Man on the moon *

If you look carefully at the moon, you'll be able to make out the face of Bungie employee Chris Carney in the bottom-right. Best seen with a scoped weapon.

Viewing this face on the moon will unlock the achievement Man on the Moon
⠀
⠀
Satellite Dish Man

On the opposite side of the map to the moon, beyond the cliffs you'll see several satellite dishes in the distance. If you zoom in on the one closest to the map, you can find a man watching you from the platform it sits on. This is apparently Travis Brady, another Bungie employee.
⠀
⠀
"HOWL"

To the right of the satellite dish with the man, you'll see a set of trees on the right-side, close to the cliff in the far distance. If you zoom in on these trees with a scoped weapon, you can just about see that they vaguely make out the word "Howl".

⠀
If you can read this, you're too close

Something you may not pick up on in the general chaos of multiplayer is the faint text on the signs attached to the heat exhausts towards the back end of the map (closest to the satellite dishes). If you zoom in on the warning signs, you can find the text "If you can read this, you're too close" barely visible at the bottom.
⠀

⠀
Halo 3 Logo

In the corridor surrounding the room where the energy sword spawns you can find a couple of security camera that will follow you around as you move. With the right angle you can just about make out a very low-resolution image of the Halo 3 logo.
⠀
‎⠀
Microsoft Windows Logo

In the room where the sword spawns you can find a telephone on the wall. Knocking it off the wall and onto its rear reveals a sticker of the Windows logo.
⠀

⠀
Valhalla Wall Messages

Several messages can appear on the Forerunner installation wall which skirts the middle of the map on the right-side as you look into the map from the lake.
I have highlighted on the map below where the messages will appear.


(Map from https://www.ign.com/wikis/halo-master-chief-collection/Valhalla )

The messages which can be found, and on which dates are as follows:

• Christmas Day: A Christmas light with an X on it
  
• Bungie Day (July 7th): Seventh Column Symbol.
  
• Halloween: A grave stone that reads "RIP"
  
• July 4: The sign reads "BBQ at Bob's Place" (This itself is a reference to Marathon, a game series Bungie worked on before Halo.
  
• Cinco De Mayo: The sign reads " Toady Was Live!"
  
• New Years Day: The sign reads "Make Love Not War"
  
• Earth Day: An image of a skull with a recycling sign.
  
• Veterans Day: An image of the famous "Kilroy was here" grafitti which was a real-life WWII meme. (Further reading: https://en.wikipedia.org/wiki/Kilroy_was_here )

⠀
Images:
⠀
Christmas
⠀
Bungie Day
⠀
Halloween
⠀
July 4th:
⠀
Cinco De Mayo:
⠀
New Years Day:
⠀
Earth Day:
⠀
Veterans Day:

Viewing two different wall signs will unlock the achievement Elder Signs

(Information and images of messages taken from https://www.halopedia.org/Valhalla_wall_Easter_egg )

This section is for miscellaneous easter eggs/Fun things of note.

Chief EG-X

Printed on the bottom of every shell casing ejected from UNSC weaponry is the text "Chief EG-X"; an obvious reference to Master Chief. Also appears in ODST and Reach.
⠀
⠀
Hippo EG-X
⠀
Similarly to the above, except this applies to shotgun shell casings, which read "Hippo EG-X".
⠀
⠀
Trogdor

The character Trogdor the Burninator can be seen on many discarded cartons of Chinese food found throughout the game. The screenshot below is from Foundry.
⠀