Towards the end of Monsters University, you find out that Sully and Mike worked for the Abominable Snowman in the mail room. But in Monsters Inc., his reaction isn't what you would expect with Sully and Mike working for him. Furthermore, his explanation of why he thought Sully and Mike are friends seems strange if he knew them back in the mail room.
When Mike and Sulley are first shown their room at the fraternity house, the light switch is under the top bunk bed. In subsequent shots it has moved closer to the door and is no longer directly under the bed.
When Mike punches the bed to show Sulley all of his shedded fur, much of it falls on his head. In the next shot, the fur has disappeared.
In the library, Greek Council sponsor Claire says there are only two teams left; but this is not true until the final event.
In the cabin scene, near the end of the movie, a record player has the record spinning in the wrong direction.
In the opening scene, when Mrs. Graves is counting students, she counts to 19 and then notices that Mike is missing, which means that there are 20 students in the class. If this were the case, he wouldn't have to pair up with the teacher. However, one of the students could have two heads, similar to Terry and Terri - though they are considered two separate entities, Mike could not conceivably pair up with one of them while the other already has a partner.
In Monsters Inc., Mike tells Sulley "You've been jealous of my good looks since the fourth grade, pal." However, according to this movie, they did not meet or become friends until they went to college together. The producers have stated that Mike was merely using an expression.
During the final scare games event a monster walks into the scare simulator. When he comes back out he is shorter.
In the house party scene, a modern dance song is played. Assuming that this movie takes place years before Monsters Inc. (which was released in 2001), this song shouldn't even exist.
Monsters University is said to have founded in 1313, way before the screams the monster world collects would've been useful for energy.
In Monsters Inc, it's revealed that Sulley's first name was James. But in this movie, he said that his name was Jimmy.
Despite the fact that Squishy's mom was listening to loud music, she didn't lose her hearing.
The textbook chapter on the Cobra Hiss explains the eyes need to be opened to 110% capacity, but the diagram wrongly depicts this as an angle with the eyes open at 110 degrees.
Don tells Sullivan that he's scary even with his pink polka dots. They're not pink, they're purple.
Terry Perry is obviously voiced by Sean Hayes while Terri Perry is voiced by Dave Foley the credits and encyclopedias mistook Terry to be voiced by Dave Foley and Terri to be voiced by Sean Hayes since Dave Foley's voice was heard from Terri and Sean Hayes' voice is heard from Terry.