Deliberate mistake: In Monsters, Inc., when Mike and Sulley walked through Monstropolis to go to the company, Mike said to Sulley "You've been jealous of my good looks since the fourth grade". In this film, we're told Mike and Sulley met in college. [In the commentary, director Dan Scanlon explained that there was a lengthy scene that would have followed Mike and Sully throughout their years in elementary school, but it would have slowed the pace of the film and would have reduced the impact of their rivalry. Rather than spend a lot of time on a back story, Scanlon decided to have Mike and Sully meet in college, even though this was inaccurate.]
Monsters University (2013)
1 deliberate mistake - chronological order
Directed by: Dan Scanlon
Starring: John Goodman, Steve Buscemi, Billy Crystal, John Krasinski
Continuity mistake: In the scene when Mike is at the school door lab. When he swipes the access card the door swings out. But when the campus police try to get in it is blocked from the inside, indicating the door opens inwards.
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Suggested correction: If you look carefully, you will see, that those are actually two different doors, which even have hinges on different sides. There's some space between them in the entrance to the lab, it can be seen just before Mike enters.
Sulley: You don't study scaring, you just do it.
More trivia for Monsters University
Question: Is Mike's dream where he says "But you are a princess and I am a stable-boy" a nod to "The Princess Bride", which has essentially that plot with a cameo by Billy Crystal?
Answer: Yes, the line "Mmm, I know, you're a princess and I'm just a stable boy..." is absolutely a nod to The Princess Bride. Though Billy's role, with all his genius improvised ad-libbing, is quite a bit more than a cameo.