Continuity mistake: When Belle finds her father locked up she's holding her stick with one hand, then the angle changes and she's using both. We switch back and she's using one hand again.
Factual error: The schoolmaster chastises Belle for teaching a little girl to read. But in 1692, a time before the story is set, King Louis XIV issued a royal decree requiring villages to establish schools and requiring all parents to send their children - boys and girls - to the village schools until they were 13 years old.
Factual error: The head master of the school criticizes Belle for "teaching another girl to read." But beginning in 1692, well before the movie is set, all parents in France were required, by royal decree, to send all their children, boys and girls, to school until at least age 13.
Continuity mistake: When Belle exits her house singing, in the front shot the building to the right in in shadow. The angle changes and it's suddenly much brighter.
Continuity mistake: When Belle gets to the castle to save the beast she's wearing a coat. Where did she get it though? When she left the village she removed the top of her dress but did not have a coat in hand. (01:42:25 - 01:46:40)
Audio problem: When the wolves attack Maurice and Philippe, the wolves make growls that only big cats (lions/tigers) would make.
Answer: She didn't have to, the second Belle proclaimed her love for the Beast, the spell was broken. She would have seen her use her magic to reverse the curse. It would be obvious to everyone she was an enchanted being.