Continuity mistake: When the evil king's female assistant is "turned into" Odette, and Prince Derek is dancing with her near the end, he puts the locket on her. The chain goes around her hair, and in the next shot, it's under her hair. They were dancing the whole time, so how could she or Derek have pulled her hair out of the chain?
Continuity mistake: When Uberta is telling Derek about the ball, she is standing by a large door. When she says that the ball is only a few friends and their daughters, she is standing right next to the door. When she turns around to tell the short footman that she wants the ball to be big, she and the footman are instantly farther down the hall and not beside the door as in the previous shot.
Continuity mistake: When the musicians are being shot at, Derek taps his arrow holder with one of his arrows and the edge of it goes red, when we get a shot further away the red mark is gone and it's as clean as ever.
Continuity mistake: When Prince Derek is leaning over Odette's body right at the end when she is dead, he stands up and says that the vow he made was for her. In the next shot he is kneeling, and in the next one he is getting up into a standing position again.
Continuity mistake: In the scene at Derek's library, when Queen Uberta comes to remind Derek of the ball, she is holding letters in her left hand. When Derek tells her he can't go, her lips start quivering and she puts both her hands up to her mouth without the letters in either of the hands. In the next shot, however, the letters reappear.
Continuity mistake: Derek rides furiously to get to Odette after King William's captain informs them they were attacked, he arrives and immediately leaps off his horse. In the next shot (as well as a later wide shot) his horse is gone, and never comes back.
Continuity mistake: Toward of the end of the film when the evil lady is dressed as Odette, when she enters the castle a small man opens the door. She winks at him, then walks in. As she is going down the stairs we can no longer see the man.
Continuity mistake: When Rothbart is doing his musical number, there are three girls from a fountain statue that are magic-ed to life to be his background dancers. In the first few moments of the song they are in statue form on a pedestal rising from the dry fountain. Moments later, Rothbart casts a spell so that the crumbling room looks new, and their pedestal is empty. Then, around the end of the first verse, he goes to bring them to life, and they're back on the pedestal, still stone.
Continuity mistake: After Derek kills the Great Animal, he kneels in front of Odette and cradles her in his arms. Look closely at his cape. The rip in the back of it changes positions between shots.
Continuity mistake: In the scene where Uberta is scolding Derek for shooting arrows into the drawing of Odette, the number of arrows stuck in the drawing changes between shots. In the wide shot, the drawing of Odette has three arrows in it. Derek shoots another arrow in it, making it four. In the close up of the drawing, only two arrows are seen, and then three, as Derek shoots another arrow in.
Answer: From what I understand it's done with a method called xeroxography. It's a really good job, I'll agree.