Continuity mistake: When Mrs. Potts puts Chip into the cupboard, the handles change style and colour: from gold to black. Also, the carvings on the wood become blue painted for a brief shot.
Continuity mistake: Beast bursts into the West Wing, uses the magic mirror and puts it on the table. A shot later it has vanished. Note the shape of the rose between both shots and you'll notice that it's not an opposite angle. The mirror is definitely gone.
Continuity mistake: When the Quiet village song ends, the sign on the last house on the right swaps from green to brown coloured between shots.
Continuity mistake: When Gaston stops Belle on her way home, the three blonde girls magically appear in the middle of the village sighing of love, then they disappear but reappear a shot later next to the last house in the village. (00:08:40)
Continuity mistake: When Belle finally walks home, the road is in the shadows. In the white angle the street is bright and sunny. (00:08:05)
Continuity mistake: When the three girls watch Gaston, the wall on their right has a chipping on the painting with visible bricks underneath. In the wide angle, the wall is fixed and the bricks are now visible in the second section of the wall.
Continuity mistake: Belle walks by the main street and the stalls, signs and number of people change between the close shots and the wide angle; check a blue pig-shaped sign called "Le jamon": a shot later it's round and brown colored.
Continuity mistake: When Gaston tries to walk between the crowd, check the way the characters have been animated: they step forward and then backwards over and over again, as if it were a loop or a bug in a videogame. (00:07:31)
Continuity mistake: During the Gaston song, when the three girls sing, the chippings on the walls behind and to the right change style between shots.
Continuity mistake: All along the asylum keeper scene, the amount of snow on the railing at Belle's home keeps increasing, decreasing and vanishing randomly.
Continuity mistake: After rescuing his father, Belle passes a cloth around his body and finally rests her hand on his father's chest. A shot later she is placing her arm on his back and the cloth is gone.
Continuity mistake: When the asylum keeper shows up, Belle's door has some black nails on the wood that disappear in the wide angle.
Continuity mistake: After Belle leaves the castle, rescues her father, and takes him home, snow suddenly appears on the stone steps to the house.
Continuity mistake: When Belle leaves the castle Beast leans on the window and howls. From a front angle he is nowhere to be seen.
Continuity mistake: After Beast lets Belle run away there's an aerial angle of her horseback riding and Beast howling with both gates open. In the close-up the right door is closed.
Continuity mistake: Beast transforms into human and says "Belle, it's me." As of then his hairstyle changes in every shot: First it's long and falling behind his shoulder. Then it partially covers his right chest, and when Belle caresses his face his hair is tucked inside his shirt.
Continuity mistake: After Beast becomes human he flies, then falls and once on the floor check the right side of his leg touching the stone floor. When the angle changes his shroud is now covering the floor.
Continuity mistake: When Beast is about to die, Belle's left arm is on his chest. Beast raises his right hand and then Belle's arm is gone.
Continuity mistake: When Lumiere becomes human the marble columns and golden ribbons by the wooden lattice disappear.
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.