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.]
Deliberate mistake: During the entire movie nothing is mentioned about the rape of Merrin until the very end, even though it is quite obvious for a forensic investigator to determine she was raped, and something like that would be very important to help find a suspect. This is done deliberately to continue the plot as rape would make Iggy less of a suspect (being her boyfriend for years) and someone like Lee more (known by Iggy and others he had feelings for her).
Suggested correction: Boyfriends (and even husbands), are routinely accused of and found guilty of raping their partner. Given that they were seen arguing and told by the waitress that she saw Ig dragging Merrin to his car, there's no reason to think the police wouldn't suspect Ig of rape. We don't see any of the proceedings and we are told only a little bit of information about how the characters got to where they are at the start in order to build suspense, it has nothing to do with continuing the plot.
Deliberate mistake: Hansel will die if he doesn't take his medicine for 4 hours, but after hanging overnight in a tree he shows no signs of needing.