Continuity mistake: When Lefou runs out of the castle, he is missing one shoe. In the next shot, outside the castle, if you look closely he has both shoes on.
Continuity mistake: In the very short scene where the Beast throws Marice into the machine and it carries him away, the front entrance of the castle is utterly different from normal. For instance, normally there are no stairs leading up to the castle, the statues on either sides of the doors are different, the walls next to the entrance are shaped differently, and so on.
Continuity mistake: At the very end, when all the objects change back into humans, the position of the roses on the walls in the background changes between shots.
Continuity mistake: In the scene where the villagers try to take away Maurice, the position of the vines over the cellar doors changes between shots.