Continuity mistake: When singing the song about what they would do if the monster came to their room in the night, Simon puts on Alvin's duvet/blanket as a cape. It then shows an imagination sequence where the blanket is a correctly sized cape to fit him. When it returns to the real world, the 'cape' is the size of his imaginary cape, nowhere near the size of the bed.
Continuity mistake: At the beginning of the movie, When the monster loses his head, it is left next to him. But in the next shot, it's gone.