Despite being offered the role of Dean Hardscrabble outright, Dame Helen Mirren requested that she audition for the role anyway to ensure that the filmmakers were satisfied with her performance.
As the students enter the School of Scaring building, they all touch the front paw of the statue in front of the building. This is a reference to a tradition at Harvard University where students touch the left foot of the statue of John Harvard for good luck. As a result, the foot of the statue of Harvard is shiny and polished down. The animators included that onto the statue in the movie as well.
There is a line in Monsters, Inc. (2001) where Mike says that Sulley has been jealous of his looks since the fourth grade. Since this movie was going to show Mike and Sulley meeting in college, it obviously contradicts that line. Director Dan Scanlon admitted that there was some conflict behind that, and even had one treatment showing Sulley and Mike meeting in the fourth grade, then skipping ahead to their university years. Pete Docter (director of Monsters, Inc. (2001)) and John Lasseter personally told Scanlon that they loved that he was honoring that one line said in the movie, but he "...had to do what was best for the story". As a result, the line was put aside and Sulley and Mike would be shown meeting in university. As a joke, Scanlon said that Mike's line in the first movie is "an old monster expression."
When James P. "Sulley" Sullivan (John Goodman) enters Mike Wazowski (Billy Crystal) and Randall's (Steve Buscemi's) room with Fear Tech's pig, a motivational poster can be seen above Randall's bed that reads "Winds of Change: Shh... Can you hear them?" Randall says the same line to Mike in the locker room during Monsters, Inc. (2001).
When waking up after sleeping on Sulley's hand, Mike is heard saying "I know you're a Princess and I'm just a stable boy." The line refers to one of Billy Crystal's previous screen credits as Miracle Max in The Princess Bride (1987) a story focusing on the love between a Princess and a stable boy.