There is a scene with Belle and Beast dining. Beast wolfs down his meal out of the dish and his face is covered with food. Belle looks shocked so Beast then tries to use a spoon and he is completely clean. Belle smiles sympathetically and Beast is covered with food in the next scene. In the next shot, they both eating directly from the bowl and Beast is clean again.
When Belle's father is lost in the forest, he looks at a sign at the crossroads that have barely readable lettering. If you look closely, you can clearly see "Anaheim" written, along with Saugus, Newhall and Valencia - all in Santa Clarita.
In the scene where Gaston tries to propose to Belle, he walks in the door and leaves it open. However, by the end of the scene, the door has magically closed itself, because Belle's back is to the closed door when she opens it and lets Gaston fall face first into the mud puddle.
Belle opens the door outward so Gaston falls out, but after she throws his shoes at him, she slams it shut from the inside.
During the end the clock slides down the stairway. At the end of the stairway is a big post, but he slides right off, never hitting the post.
About 10 to 15 minutes in the movie you see Gaston shooting his shotgun into the air at a flock of birds. In the next frame instead of seeing shotgun pellets flying through the air you see a half dozen arrows flying through the sky and killing one of the birds.
If the story takes place sometime during the middle of the first movie, where do the new characters go that were added in the second movie?