Factual error: After Gaston stabs the Beast in the fight sequence, there is no blood shown on the knife. [This is a longstanding Disney animation tradition. The House of Mouse seems to believe that onscreen violence is less traumatic if all evidence of it disappears quickly. Thus, you rarely see blood and when it IS seen it's usually minor, even if the wound isn't minor.] (01:16:15)
Continuity mistake: When Cogsworth comes into the study to say that Belle isn't coming for dinner, he opens the door inward and doesn't shut it. In the next shot of the doors from the hallway, though, the doors are closed, and the Beast opens both doors outward. They aren't double-swing doors like the kitchen ones. (00:32:30)
Continuity mistake: When we first see Belle at the beginning of the movie, there's a bridge in front of her house, which she crosses over to get to town. But later, after Gaston plots with the insane asylum keeper, there's a wide shot of Belle's house with a horse and buggy waiting in front, and the bridge is gone.
Continuity mistake: When Gaston enters the West Wing with his bow, the painting on the right side of the door is different than it is at all other points in the movie.
Continuity mistake: When Maurice looks up at the castle after he has just arrived, a lion's head is carved over the front door. But when Gaston leads the villagers to the castle later in the film, the lion's head has been replaced by a green shield.
Deliberate mistake: In the brawl, one of the villagers gets his teeth knocked out, but his teeth are intact again a few seconds later.
Continuity mistake: In the 'Human Again' song, near the end of the song Cogsworth and Lumiere turn on the fountain and the large middle statue sprays out water, but the two statues either side of the middle one are turned off. Then the wardrobe jumps out onto the balcony singing and then it cuts to an ariel shot, and now the two side statues are suddenly spraying water too. (00:58:45)
Continuity mistake: When Maurice is tossed out of the tavern we get a nice view of the front with its large hanging sign, but after Gaston whispers his plan to LeFou once again we see the front, which is quite different. The sign is gone, and now there are horns hanging on the awning, etc.