Continuity mistake: When Mike is bringing Sully to the fixed door he has no slivers or band-aids on his hands, then when he says "it was a lot of wood to go through" you see he does.
Other mistake: Near the end of the film, when the identity of 0001 of the CDA is revealed, number 0112 is shown both standing next to 0001 as she enters the room and behind Sully and Mike on the opposite side of the room.
Other mistake: When Sulley and Mike take Boo into the Factory, they see all of the CDA agents. There are 3 talking to Mr. Waternoose(as we see seconds later). One of them is number 00002. When they are done, they escort Mr. Waternoose to somewhere else. However at that very second another agent comes in with a metal detector thing. His number is also 00002.
Continuity mistake: After the Scare Floor shuts down at 6:00 and Sulley goes back to do Mike's paperwork, the clock reads 5:48. After he returns again to put Boo back, it clearly shows 5:48. Finally, after Randall leaves and Sulley leaves the Scare Floor for the restaurant, the clock reads 6:48.
Continuity mistake: At the beginning when you see the monster in the testing room from under the bed with the glowing eyes, you also see the soccer ball on the left side of the screen. This shot takes place on the side of the bed. After the monster gets scared, he backs up kicks the soccer ball, but it is now at the foot of the bed in the middle of the room.
Continuity mistake: At the beginning when the monsters are at the testing room, you can see the boy in the bed seeing something opening the cabinet. He closes his eyes and opens them up again to see a sweater sticking out. But when another monster sees what he does wrong on the tape, the sweater isn't sticking out anymore.
Audio problem: When we see Mike during the slumber party, we hear seven bells ring for the seven filled cylinders, but there are only six cylinder-filling noises.
Continuity mistake: In the opening scene, on the floor there is a toy train on circular tracks when the monster sneaks in. When the monster trips backwards over the ball and skateboard then falls onto the jacks, the train and tracks are gone.
Deliberate mistake: When Boo laughs repeatedly while playing hide-n-seek with Sully in the men's room, nothing happens to the electricity - no surges as with all other times she laughs. [In the audio commentary by the directors, they explained that it would've been distracting if an energy surge occurred every time Boo laughed, so they simply didn't address the issue. A reasonable course of action, but still a mistake.]
Continuity mistake: When Boo is in Mike and Sully's house, there's a "jazz" poster on the wall near the door, but when Boo is crying, it's gone.