Continuity mistake: When Belle is taking her book back in a basket at the start of the film, its colour changes from red to blue, back to red, then purple in the book shop owner's hand, then finally red on the shelf.
Continuity mistake: At the end of the movie, Belle shows the Mirror to Gaston and the other people in the village. She's wearing a white apron over her blue dress. When Gaston takes the mirror from her, the apron is gone. A few seconds later, it's back.