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.)
Factual error: In one of the train cars on the way out west, upon being asked by one of his henchman, "When are we going to eat the mice?" Cat R. Wahl replies, "Which would you rather have, the crouton or the entire Caesar salad?" Caesar salad was not invented until the 1920's and the movie takes place in the late 1800's.