Deliberate mistake: As Christine approaches the Phantom in his lair (just after he has abducted her), we see that she is wearing very dark black eye-shadow. Back in the dressing room after coming off stage, as she talks to Raoul, we saw her face in close up and she was not wearing any eye-shadow at all, even though the Phantom leads her through the mirror just after she has managed to slip on a robe over her undergarments and she has not yet changed to go out to supper (Raoul says she is to be ready in 2 minutes). Her hair becomes 'bigger' and wilder, too. The change in her appearance is a reference to her descending (voluntarily, I might add - he didn't drag her through that mirror) into the Phantom's dark existence and to her sexual awakening.
Continuity mistake: After being abducted during the Don Juan performance, Christine changes into the wedding gown and the Phantom places the veil on her head. The veil gets thrown aside by the time Raoul arrives. Between the time Christine leaves and the mob arrives, there is a shot of the mannequin with the veil perfectly positioned on the head (although it is highly unlikely that someone took time to put it back.) When Meg walks through the lair and retrieves the mask, yet another shot of the dummy shows that the veil has disappeared.
Other mistake: During the gypsy fair, when the young Phantom is hurriedly pulling the bag back over his head, you can see the actor's face from the side, through the bars of the cage. There is no deformity, even though the angle of the shot shows the top right of his face, where the mask is always worn later. Even moreso: his deformity is bumpy, and the side of his face is all baby smooth.
Factual error: Raoul is the Vicomte de Chagny and he gets called that throughout the movie, even during the auction (which shows he didn't change titles when his parents or his brother died, for example). Yet Christine's tombstone calls her a countess when it should have read viscountessor, even better, vicomtesse.
Continuity mistake: At the end of the music of the night scene, the Phantom lays Christine down on the bed and sings the line, "help me make the music of the night." While singing this, he moves his finger down Christine's jaw line, and his finger comes off her chin. Yet when the camera angle changes, he is just starting to move his finger down her jaw, starting up near the ear. He wouldn't have had time to move his finger back up that quickly.
Continuity mistake: During the Masquerade, there is a close-up of two of the dancers, who sing "But who can name the face?" while standing next to each other, without moving. Next shot, they are several feet apart and the lady is dancing towards where the male dancer is standing.
Continuity mistake: When Raoul is tied to the gate, the ropes across his chest change frequently. Sometimes there are 3 running parallel to each other, from his shoulder to the waist. Other times there is a big knot in the top rope. Still others there appear to be 2 ropes across with a third running straight down his chest between them.