Other mistake: Towards the beginning of the film, the teacher counts 19 students then says one is missing, implying there are 20 (including Mike) However, Mike ends up being paired with the teacher, despite there being an even number of students and therefore everyone should have a partner.
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.
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.]
Continuity mistake: When Sully first pulls the folder out for the child he is supposed to be scaring during the last scare game against Randal, the girl's fear is first listed as "Thunder and Dogs." But upon full zoom in and focus, it says Thunder and Lions.
Plot hole: The first team that gets eliminated in the scare games cheats but Dean Hardscrabble hardly seems to care. Oozma Kappa cheats and she has all of them expelled.
Continuity mistake: When Mike and Sully move into their bedroom at the fraternity house, the door opens inwards. When they fall through the doorway, it opens outward.