Factual error: There's a scene where Belle's father is riding away in the snow on his horse - the tracks left behind by the horse are exactly backwards. The round part of a horseshoe is at the front, not the back. (This was a deliberate 'in joke' done by the animators.)
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Suggested correction: It is Belle who rides the horse in the snow, not Maurice. If we're talking about this being a mistake, then it could be a deliberate mistake, but if this was truly done as an in-joke, then I think it falls more under trivia. The tracks being backwards is factually incorrect, but it doesn't really fall under the category of "mistake" if it was deliberately done as a joke.