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: The Rose started wilting at The Beast's 21st birthday and could have presumably started wilting years before the first time we saw a petal fall off. Given the fact that Lumiere stated that they were living with the curse for 10 years, prince Adam could be 23-24 years old at the time of the original movie,13-14 at the time of the curse, and the Rose could have been wilting for two to three years. This is my best guess given the approximate age of Prince Adam in the ripped up portrait before he was the Beast.