These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alternative Character Interpretation: Randall Boggs. Him leaving Mike: was it out of a desire to fit in and be accepted, or did he never really think of Mike as a friend? Mike never confronts Randall over his behavior, they just sort of drift apart, so were they friends or just roommates who got along well? Him putting down the Oozma Kappas, was it out of peer pressure, or just sadistic bullying? Is Randall really friends with Roar Omega Roar, or are they just a means to an end for him to be the best? Did he want to keep up his friendship with Mike even after joining ROR?
Author's Saving Throw: Probably. The film establishes that other Scare companies other than Monsters Inc. exist perhaps to indicate that Scarers who couldn't adjust to Monsters Inc. switch to Laugh energy didn't all suffer unemployment. Now granted, it's not as if Monsters Inc. said that it was a complete switch to Laugh Energy.
Award Snub: While not necessarily great enough to be top-tier Pixar, quite a few were surprised that the film failed to reap a nomination for Best Animated Feature in 2013, given how it was marginally more well-reviewed than both Despicable Me 2 and The Croods. To some, this is especially galling after Brave (a generally less acclaimed Pixar film) actually managed to win the Oscar the previous year (when many thought it deserved to lose to Wreck-It Ralph).
Broken Base: Some fans see this as sub par to the original movie, though others do like this movie because it doesn't override the happy ending of the original. Others have noted that the drama is impaired considering anyone who watched the original film would know that Mike and Sully are striving to join an industry fundamentally based on a lie.
Other fans had no problem with the movie itself, but rather with under which circumstances it was produced. It was originally going to be a sequel to the original movie, but was scrapped to instead make a prequel of the main characters' school days. It's pretty clear that the movie wouldn't have gotten so much flak had the fans not known about this fact. Another common complaint is Boo. Those who pan the movie thought that They Wasted a Perfectly Good Plot of Boo being an older child and how she would maintain to the Monster World, while those who are okay with University thought that the ending of the original movie was perfect and having any further exploration of Boo would have ruined it.
Fans either thought the movie had a Broken Aesop, or others thought that it was brutally honest and healthy in manners of the Brothers Grimm philosophy ("You don't always have qualities to live your life-long dream, but you'll eventually find your calling.")
Fans who liked this movie thought that the comedy was a relieving breath of fresh air compared to it's predecessor's tense and dramatic tone, whilst others dislike this movie for this exact reason.
Crazy Awesome: Art. Kicking things out of his way with a crazy laughter and supposedly having been to jail are a few juicy examples.
Johnny Worthington III. Word of God wanted to convey through his decorated frat house that Johnny is deathly afraid of failure and his reputation was at stake.
If it weren't enough that Randall was already this in the first film, it just intensified once they saw him in the prequel, where people just can't get enough of making him sympathetic.
Elimination Houdini: The Oozma Kappa team actually fits this trope very well despite not being in a reality TV show. At the start, they clearly did not have the skills to compete with the other fraternities and, were it not for one fraternity being caught cheating, would have been eliminated right off the bat. While Roar Omega Roar continues to outclass them, they continue to make it to the final round by beating just one team. When they finally get their act together, with the exception of Mike and Sully, they do show the other students that they are Scarer material.
Claire Wheeler, the snarky goth girl announcer of the games. Helps that she's voiced by Aubrey Plaza. Her co-commentator, the hammy and hyperactive Brock Pearson is just as popular. The two of them together are also a popular shipping couple.
Dean Hardscrabble is also very popular with the fans. Even many of the film's critics have praised her as one of the best parts of the movie, citing her imposing design and Helen Mirren's performance.
That poor slug who takes the entire movie to get to his first class!
If you ask a fan which Oozma Kappa member is their favorite, their answer will probably be Squishy. Others will prefer another member or like all of them equally.
Well, current-societal-attitudes unfriendly, at least. You can be successful without a university education if you work hard and make your way up through the ranks over time. Not really a negative one at all, since it's not as though it's telling people to slack off; Mike and Sulley's path is harder than that of the graduates, though they make it eventually.
The film also has a more brutally honest message: No matter how hard you try or how much you love and know about the material, there are just some things in life you can't do, much like the message of Wreck-It Ralph. Accept it, and find where your real talents lie at. This is balanced out by the fact that Mike's knowledge of the Scaring world wasn't in vain and did assist Oozma Kappa in achieving their dream.
A rather broken message in that the Oozma Kappa monsters do ultimately become successful scarers through a combination of hard work and sheer ingenuity. Mike is the only member never to do this, sticking with the standard "jump out and say 'rawr' method" and giving up when it fails him miserably.
The film often shows that, yes, cruel people have a point. Jerks like ROR are correct in pointing out Oozma Kappa lack traditional Scaring build (but clearly wrong for belittling them). In a sense, this notion drives Oozma Kappa to look further to prove that traditional build is not all there is to it.
This point has more weight given the last thing Worthington tells Mike right before their last match at the Scare Games. He tells Mike "Don't take the loss too hard; you never belonged here anyway." But for once, there is no tone of malice in his voice when he says it as opposed to everything else he has said to Oozma Kappa prior. He says it in a sincere, matter-of-fact tone that denotes that he is aware about the fact that Mike just isn't scary and that Mike should realize that.
Germans Love David Hasselhoff: The film did especially well in Japan, where it grossed over $90 million in its box office run. The colorful, adorable monster designs must have done it for them.
In this film, Mike is constantly being told that he is not scary and thus can't be an on-field worker for Monsters Inc despite it being his dream. The fact is driven home when he is seen only as a funny guy by the kids he tries to scare when he sneaks into the human world. However if you remember at the end of the first film, he gets to be an on-field worker precisely because he is funny. In other words, he was able to live his dream, though in a slightly different roundabout way, because of his "flaws".
In the first film, whenever Mike and Sulley talk about breaking the scare record, always say "we" rather than "you" or "I" respectively. After this film, it's very clear that Mike and Sulley really are a team when it comes to scaring.
Hilarious in Hindsight: People who've seen the cartoon Aaahh!!! Real Monsters along with Monsters Inc. might get the idea that both the cartoon and the film have similar plot settings since both involve monsters who need to scare in order to collect energy for their society. Come Monsters University, the setting is even more similar to the cartoon as it involves monsters going to school in order to learn how to scare. Mike and Sulley even fill out roles similar to two of the three main characters of the cartoon. A super studious and hardworking student that relies heavily on books, and another student who is generally lazy but pressured with living up to the family legacy of being the best scarers.
Ho Yay: The scene where Mike dreams about kissing a princess and wakes up kissing Sully's arm, anyone?
Sulley. Although, he had lied and cheated by tweaking Mike's scare level during the final Scare Game, he was at least upfront and honest about it to Mike and the Dean, facing expulsion and rejection. It turns out that he did it because he was deathly afraid of failure and did feel that he couldn't let O.K. down.
Some are blessed with the conventional path to college (Oozma Kappa), though others can take less conventional routes to their dreams without the college route Mike and Sulley.
Just because you eventually surrender your lifelong dream does not mean you have to surrender your interest, and there are alternatives to serve your interest.
Insults can lead to inspiration and positive change. You have to know how to turn it around and make use of such of it.
Strangled by the Red String: Don and Squishy's Mom, albeit played for laughs. While their pairing up is obvious due to similarities and proximity and they likely knew each other for a time, there is only one scene of amorous affection, and then they get engaged. Though this might have been a device to indicate that a significant, but ambiguous, amount of time passed since Mike's and Sully's arrest.
Those who were expecting a tragic and sympathetic backstory for Randall were greatly disappointed. In addition, the film barely fleshes out Johnny Worthington's fear of failure, as Word of God suggests.
Celia is nowhere to be found (aside from a brief shot of a picture of her in Mike's locker near the end), which is especially conspicuous due to her strong resemblance to the girls of PNK.
Terri and Terry. They had potential to be really interesting, but after their introduction, not much is done with them. Some people don't think that it's because they are "boring character(s) with little use". Granted, their lack of Character Development left space for Fanfic Fuel.
Not making Terri female, for some. Particularly odd because of the skewed gender ratio of the film, which Pixar has been trying to avert recently, and because Terri is a popular girl's name. This has some justification in that fraternities are supposed to be male-only, with sororities being the female counterpart... although co-ed fraternities do exist in real life.
Although they work quite hard, the Oozma Kappa's motivation to join the Scaring Field isn't quite fleshed out like Mike's motivation.
The Woobie: Mike is made to be this from the beginning. Nobody expects anything of him and even his own cousin doesn't want to partner up with him. The film keeps making it worse by everyone constantly telling Mike that he will never be scary and that he doesn't belong in MU. But, despite all of the insults and put-downs, Mike still stays on top, making him an Iron Woobie.
The Oozma Kappa. They're nothing but genuinely nice, and endearingly Adorkable guys but they get the short end of the stick because of their cozy, fluffy "loser" behaviour. They get treated better later.
Randall is this before he ditches Mike for ROR, mind you, being an insecure nerd who genuinely attempts at making friends.