Revealing mistake: At the very beginning of the film, we see the transfer vehicle carrying Jack driving down the road. You can tell in several shots that the (fake) snow isn't really falling, but is just being blown in front of the camera from off-screen, especially since there's no snow hitting the road, and it's coming from the side, not above.
Continuity mistake: After Crocker discovers that Gregory is in his house, she tries to hand him the key to the basement at the Hotel. In one shot, when facing Crocker, the handle of the key is facing him, but when the camera is facing Gregory, the key's handle is is facing her.
Plot hole: In the waning seconds of the championship game, the Huskies are down by 2 and UMass has the ball. Not only do the Huskies not intentionally foul to stop the clock, but UMass attempts to run a play and set up a basket when they simply could have dribbled out the clock and won the game. Both these strategies go against what any basketball team would do in this situation, especially in a championship game.
Other mistake: When Mimi wants to dance, and she wipes the diner table clean, the table is about 2 feet square. When Mimi and Jimmy dance, they are 6 feet apart, despite dancing on that small table. (00:39:00 - 00:39:40)