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.
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.
Continuity mistake: In what is supposed to be a time-lapse scene, we see the Monsters University campus as nighttime ends and the sun rises. The shadows of the trees and buildings never change position as the sun gets higher in the sky.
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.
Continuity mistake: At the start of the movie Mike is on the second to last step, but in the next shot he is on the last. (00:05:15)
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.