Continuity mistake: When Mia and Michael are talking and Michael asks Mia to come and see his band, keep your eye on the background. You see Lily running to catch up with them and she passes in between two people and doesn't even look at them, then in the next shot she passes them again, points at the boy who has stepped to the side and says "Not you, I don't even know you."
Continuity mistake: Right at the start of the movie, when Mia is shown opening her window blinds, there are some books on a shelf to the left. The lowermost is Jane Austen's "Pride and Prejudice", which her grandmother will first give her much later in the movie, together with a rather large book ("The Vanderbilt Complete Book of Etiquette"), in which Mia has already been reading in the immediately preceding scene.
Continuity mistake: When Mia is leaving right after she starts dance lessons with Joe, you see her running out of the shot and in the next shot she already has her backpack on. It seems impossible for her to have grabbed it and put it on while continually running in such a little time span.
Continuity mistake: In the beginning of the movie Mia slides down the pole to get to the main floor. The next shot is her mom coming down a ladder to the ground floor talking to Mia, but you can see the top of Mia's head in the foreground as she walks down the staircase. Supposedly she's already on the ground floor via the pole.
Continuity mistake: When Mia and Queen Clarisse are careening down the hill in Mia's Mustang, you see she hits the trolley on the green part and puts a HUGE dent in the side of it. Later in a different shot, you see the trolley and the green part has no dent, and the car is much to low to have hit the trolley in the green part in the first place.