Continuity mistake: When Gaston and Le Fou approach the village on horseback, they watch Belle through a telescope. In the shot from behind, Le Fou has to stretch out to reach the telescope when Gaston passes it across and his fingers barely touch the end of it, but when the view changes to the front the horses are closer together and he is holding the telescope firmly in the middle.
Continuity mistake: In the opening song "Belle" - Belle exits her house wearing brown lace up boots. When she then helps the little girl to read, she is wearing espadrilles. When she leaves her house to sing the reprise "Madam, Gaston, can't you just see it" she is wearing espadrilles. Later when Phillipe the horse returns without her father, Maurice, Belle is wearing brown boots again and enters the castle wearing them. Then when she is with the beast and stood on the ladder choosing books - she has espadrilles on again. Her shoes alternate throughout the whole film.
Revealing mistake: When Belle exits her house, the reflection on the window by the door shows a rectangular flat roofed building, nothing to do with the old gable roof we see in further shoots. In the making-of we are revealed that the prop building is in fact rectangular and flat, with a green screen on top to allow for the CGI.
Plot hole: The wolves seem to conveniently make an appearance to further the story, only to disappear in other parts. They are their for Belle's dad at the beginning and Belle when she tries to escape the castle initially. When Belle's dad leaves the castle after Belle takes his place and when Belle is freed to save her dad, they are not there.