The college prank Sulley plays on Mike in one of the teaser trailers: sticking foil all over him, then turning out the lights and hanging him up as a disco ball.
Mike's mumbling in his sleep, which is mostly followed by giggles. And we see Sulley looming up on him with a bottle of Monster glue named "GLEWW" with a mischievous smile on his face.
"Class President? Ha...Ha..."
"I can't go to school, I am not wearing any clothes..."
"My pony made the Dean's list..." (this one was apparently the fan's favourite, and Pixar artists actually drew the literal pony with Mike in Monsters University for Mike's dream!)
"My homework ate my dog..."
And then followed by the other monsters partying outside Mike's room until he comes out, and they use him as a makeshift disco ball.
AND then we see Mike being strung up as a disco ball for a quiet dance, with Sulley eating chips and saying, "I love college." and snapping a photo of Mike.
In the prologue, "Frightening" Frank McCay the Scarer's reaction to the Monster Inc staff all crowding around him with fire extinguishers, first aid boxes, walkie-talkies, frozen with anxiety and fear plastered on their faces, was a rather flat and deadpan, "what?"
This gem is mentioned in the Junior Novelization of Monsters University: This line is actually vaguely heard in the movie.
"Let's go break in somewhere else!"
and one more, also from the same book:
Mike: Ok, pop quiz time! What's more scary than a human child?
Art: "raises his hand" Two Human Children?
Art jumping into a bunch of poison needle balls and hugging them, screaming, "I want to touch them!". You can pretty much guess what happens next.
Don's wonderful cursing when he accidentally stepped on the poison needle balls. Cue Squishy covering his ears.
"Cheese and Crackers!"
"Son of a Mustache!"
Terri and Terry also got hit by the poison needle balls too. Terri's reaction to Terry's swelling head was priceless.
Squishy being hit by enough poison balls to make him puff up like a ball (Big time!). He accidentally swallowed one (because a jerk spectator threw one in his mouth while he was screaming), and the rest of the OK gang has to roll him out of the obstacle course.
Then there's the scene where Oozma Kappa is trying to avoid being caught by Monsters Inc. security.
Sherri: Seatbelts! Everyone fastens their seatbelts. Squishy: Okay, go! Sherri: Does anyone want gum? Squishy: JUST DRIVE!!
When she drives the Oozma Kappas on their "field trip" to the Monsters Inc. factory, she waits in the van "listening to her tunes." Said "tunes" are "Island" by Mastodon.
If you pause the trailer at the right moment, you see Randallholding a tray of cupcakes! Said cupcakes each have a letter arranged to spell "be my pal"! And if you watch Monsters University in another language, the cupcakes have icing on them, which is essentially Randall's eyes, glasses and a smile.
For more Randall fun, look at his side of the room in this clip. He appears to have designer sheets and a luggage set. Not to mention slippers of his own face.
Even better, if you look closely at his motivational poster, you can see that it says "The Winds of Change," and, under that, "Shh... You hear that?"
At the social, Mike rides the Fear Tech mascot pig and bumps into Randall, who tosses the cupcakes into the air and land on his face to form the word "LAME".
Who then literally bulldozes through to the end of the field, dragging a whole bunch of other players behind him, and knocks over the goalpost for good measure.
Many of the club members at their booths during Orientation Day are a hoot, for those alumni who remember how much they stood out. The Art Club booth member dunks his head into some paint, and sloshes it onto a canvas.
Mike: We have everything to win right here. *points at his chest*
Mike: No, me!
Mike to Sulley: "It's an obstacle course, what are you gonna do? Roar at it?"
And this gem:
Mike: I am going to beat you over the finish line.
Sulley: Get ready to eat my dust.
Squishy: Hey guys, should we huddle up?
And later...when they crossed the finish line:
Sulley: Take that, Wazowski!
Mike: Are you delirious? I beat you!
Note that Mike is pointing a finger upwards at Sulley, and because his finger is puffed up, it looks like he's flipping Sulley the bird.
Roz's cameo as the head of the CDA, telling the school that she's always watching.
George Sanderson's Butt Monkey status is shown in this movie too. His fraternity was disqualified from the first event because they used anti-poison gel. Then a referee uses a poison needle to puffen up Sanderson's leg. He did not enjoy the feeling.
Don Carlton getting engaged to Sherri.
Also, his awkward and increasingly uncomfortable way of describing his new relationship to Squishy as a result.
"Think of us as brothers who share the same mother/wife. No, wait, that's even worse.
And then throwing a student monster who accidentally made a noise out of the library and into a nearby river.
For that matter, Mike, Art, Squishy, Terry, Terri, and Carl sneaking through the library while Sulley follows them with a frown. At one point, Sulley looks close to flipping his lid.
After Mike and Sulley are kicked out of the scaring program, Sulley follows Mike around glaring at him at uncomfortably close distances. The best, however, is when Mike goes into his room; Sulley, rather than following, just stands outside the door and glares at it, waiting until Mike emerges so he can continue glaring at him. How long, exactly, was Sulley planning on standing out there?
The RA's. For anyone who went to college and stayed in the dorms, it's both hilarious and irksome that they are just as Keet and as genki as in real life.
Also, all the RA's name rhymes. (They are known as the Smile Squad).
They are named Jay, Kay, Trey, and Fay. (in order) There is a fifth member who is stationed at the dorms and assigns new students their room, but he wasn't named.
According to the Monsters University Fearbook, the last member is named Ray.
Chet's response at the end of this exchange.
Worthington: When you lose, everyone will forget about you. Mike: Maybe so, but when you lose, no one will let you forget it. Chet: Wow... That's actually a good point. (Worthington then dope slaps him)
Oozma Kappa getting covered in paint, glitter and stuffed animals, with the photo being posted all over campus. Bonus points for the picture being on Chet's coffee mug. Better bonus for all of the Oozma Kappas looking surprised and mortified, except for Art, who is smiling.
Training for the 'hide-and-seek' competition (Mike calls out their methods of hiding):
"Kiosk! Pile of leaves! Standing out in the open!"
Art was the one standing out in the open, staring at a butterfly, not moving at all.
Don: "Thanks! I cannot get down."
The swinging-out boards painted with human teenagers on them in one of the monsters' Scare Games competitions, "Don't Scare the Teen".
Even better is the fact that Carrie breathes fire at the latter board in anger at PNK's disqualification by instinctively scaring every teen board, as if she's thinking "SHUT UP!"
Waternoose's cameo at the end of the film, in which he has an afro and facial hair.
Mike using Sulley's hand as a pillow, and was about to kiss it when he woke up. And when Sulley falls out of his top-bunk bed and wakes up in a panic: (paraphrased)
Sulley:What are you doing?!
Mike: "Your grubby paw was in my bed!"
Sulley: "Were you kissing my hand?!"
Mike: "Hahaha...no, what about you and all your shedding?!"
Sulley: "I don't shed."
Mike: "Really?" [hits his bedframe and a shower of Sulley's fur comes raining down]
Claire (the three-eyed goth Scare Games host) cheering and going wild at the end of the final challenge after spending most of the movie looking bored.
Claire: THEY DID IT! AAAAAAGGGHHHHH!
This doesn't do it justice. She spends the entire movie looking incredibly annoyed at her extremely energetic partner, saying almost everything in total deadpan. When Oozma Kappa win she tackles him out of the frame and jumps up and down like an over-excited sports fan.
Mike trying to stop Johnny from selling the "Cute-ma Kappa" picture.
Mike: "What are you doing?"
Johnny: "I'm raising money for charity."
Mike: "Stop it!"
Johnny: "You want me to stop raising money for charity? That's not cool."
Chet: "THIS GUY HATES CHARITY!"
Little Mike calling his teacher, Ms. Graves, by her first name and her response:
Karen: Please don't call me Karen.
Word of God says that Dean Hardscrabble was a member of Eta Hiss Hiss. The Goth sorority.
Initiation tour guide: The MU cafeteria has some of the best chefs in the world!
A large purple gelatinous lunch lady monster picks up the trash can that students have been throwing away their food in and dumps it back onto the food counter.
and THEN the monsters standing there began to dig in with relish.
In Mike's "Up to the Final" montage, he is cleaning the floor with a drivable cleaner while studying. Without noticing, he sucks up a furry monster, and it comes out looking like a puffball. Can be seen just after the 30-second mark here. And many other students were either diving out of the way or getting knocked over by him.
When Dean Hardscrabble is asked to give the obligatory "words of inspiration" speech, not only does she only put pressure on the Scare Program students, she gives us this when she has finished her speech:
Dean Hardscrabble: I hope you are all properly inspired.
When Mike is about to meet his new roommate and reminds himself that he is "about to meet the bestest friend I'll ever have". We're suppose to expect Sulley, but when he opens the door, we see the silhouette of Randall Boggs. However, despite the menacing silhouette, the Randall is overly polite to Mike.
Terri: "I'm a dance major!"
Terry: "And I'm not."
Terri: "Oh, now you're embarrassed, just because it's in front of people—"
Terry: "You should wake up embarrassed."
There's just something funny about Sulley explaining who ROR are and then throwing Mike under the bed to fetch Archie.
Sully "They only accept the highly elite. Okay, I'll lift the bed and you grab the pig."
Note that Mike's scream of pain is the same as the ones he has in the first film.
Scream Canister Design class is hilariously boring, especially with Professor Brandywine's design that captures a boring professor. He even takes a huge boring breath.
At the start of the class, Brandywine holds a traditional speech about how "some people consider scream can design boring; uninspiring; no place for a self respecting monster" - only to then fail to pay it off, and just tell the students to open their books. It makes it clear that he's one of those people too.
The big ear-to-ear (or perhaps, horn-to-horn) smile that Little Mike has when he walks out of the child's room on his field trip to MI.
Claire and Brock advertising the scare games.
Claire: You could totally die. Brock: AND IT'S WORTH IT!
When that year's Academy Award nominations were announces and the film was notably absent from the list of Best Animated Feature nominees, director Dan Scanlon responded by simply tweeting "Tuxedo for sale."
One from the short: Sherri's turn at "door jamming" - jumping through one portal and out the other. She goes through the parents' room, in slo-mo, on fire, curlers, housedress, and all. It's the boggled humans' expression that sells it.
The parents asking their little boy if they could sleep in his room because of the monsters, and the exasperated kid going "That's what I've been trying to tell you!"
The official Monsters U website, aside from being a perfect university-homepage pastiche, includes profiles of the Oozma Kappa gang. From Terry and Terri's interview, we - and Terry - learn that Terri likes to relax by watching Terry sleep.