Continuity mistake: When Mia and her grandmother enter in the ballroom together at the end. Mia's mom and her date are clearly standing in front of the band, but when Mia is looking for someone to dance with, they are standing beside what looks like curtains. Then as Mia and Michael start dancing you see her mom back in front of the band.
Continuity mistake: When Mia is in her room preparing to run away, there is a shot of Fat Louie in his carrier, and there is a white spot around his eye. In the rest of the movie he doesn't have a spot on his eye. This is because in the making of the movie there were 4 different cats used to portray Fat Louie. Still a mistake though.