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.
Long time fans of the series will be very interested in this psychologist's assessment of the main characters and their relationships with each other. Interesting highlights include attributing Randall's Jerkass behavior to Compensatory Narcissistic Personality Disorder and intentional emotional manipulation by Waternoose, as well as pegging Mike as being a legitimate psychopath. Seems like Epileptic Trees at first, but reading the full article has the potential to blow minds.
Crowning Music of Awesome: "If I Didn't Have You", which won the Oscar for Best Original Song. And after Randy Newman had suffered almost 20 non-winning nominations up to that point.
Also Enter the Heroes and The Scare Floor. Setting up for a big job, then having a lot of fun doing it.
Draco in Leather Pants: Randall. A good number of his fans are convinced that he was just stressed out and didn't really do anything wrong. The more extreme ones see him as an orphan who's descriminated against for being a reptile, both in-universe and out. Any and all material that contradicts these views is immediately deemed non-canon or just ignored.
Fridge Logic: Boo's laugh activated all the doors in the Door Factory. Realistically, at least one human would have opened their door at the time to see that they had just entered the monster world; exposing the monster world to the humans.
Harsher in Hindsight: Randall's behavior in the original film becomes worse, not to mention much pettier, when you watch Monsters University and realize that for months, if not years, he'd been beaten out as Scare Leader by a college dropout!
Randall's nastiness towards Mike becomes this after Monsters University: not only did they used to be friends, or at least friendly roommates, Mike's advice to Randall to use his invisibility is what helped him become such a good scarer in the first place.
Also, Mike's bitterness over the possibility of losing his job reflects all the hard work and turmoil he had to go through to have his job as a Scare Assistant.
Memetic Mutation: Waternoose's line, "I'll kidnap a thousand children before I let this company die!", which was translated in Latin Spanish as "Robaré los necesarios para salvar esta compañía" is wildly popular in Spanish-speaking Latin countries and social networks, with variations such as "I'll steal a thousand contents before I let this fanpage die!".
Also popular in the Latin american countries and related to the dub is the line "well, a kid flew right over me and blasted a car with its laser vision." dubbed as "Un niño flotó sobre mó y voló un auto con su rayo láser", made funny by the argentine-like accent used rather than by the content.
"Put that thing back where it came from, or so help me!"
Mike Wazowski on his own could be considered one on Tumblr.
Moral Event Horizon: Randall and Waternoose's plan, which involves kidnapping children and using the Scream Extractor to suck the screams from them, which if the effects on Fungus are considered standard, would kill them through suffocation by sucking the very air from their lungs along with the screams. At least Waternoose has a reason: he wishes to keep the company going to provide monsters with their power, making him more of a Well-Intentioned Extremist than Randall could ever hope to be.