Continuity mistake: After Maurice is thrown out of the tavern Gaston whispers his plan to LeFou, and when they begin to dance we see an angled wall with a dart board, bow and arrows, but the problem is that angled wall with the dart board, bow and arrows did not exist in the overhead shot, right before Maurice walked in.
Continuity mistake: When Belle is reading her book before Gaston walks in to propose, the bellows hangs from a hook on the fireplace stones under the mantle, but when Gaston is talking to Belle the bellows now hangs directly from the wood mantle, though it's back to the original way when Gaston knocks over the rocking chair.
Continuity mistake: During Gaston's song, when they sing "Give five hurrahs, give twelve hip-hips," LeFou's beer tankard switches from his left hand to his right hand, between shots. Additionally, one of the wall's wood beams near the fireplace has vanished behind LeFou, then reappears. The same thing happens again later, after they toss Maurice out the door.
Continuity mistake: Right before Belle's father enters the tavern, watch the bar on the left: First there's just one man. The father enters and a bartender plus a guy next to him appears. Then Gaston asks "Who's got Belle locked up in a dungeon?", and all three disappear. Then the father says "A beast", and the bartender and first villager appear, but not the second man.