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 the "No One's Great as Gaston" song (in the tavern) Gaston uses his blunderbuss to shoot three holes (three separate shots) in a barrel of beer. But a blunderbuss is a single-shot weapon. He would have to shoot, reload, shoot, reload, and shoot. (00:27:40)
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)
Answer: In the prologue, it states that the Beast must find true love by his 21st birthday, and that he had been cursed for ten years, so since his relationship with Belle takes place as the deadline approaches, he must have been 10 when he was cursed.