Factual error: In the film, most of the characters don't wear nearly enough stage makeup. In "Think of Me", when Christine is performing in front of a packed auditorium, for example, she would have needed a lot of blush, eyeshadow, eyeliner, etc. just to look "normal" from the audience's perspective. Instead, as you can see by watching the film, she looks pale and washed out.
Audio problem: During the end of "Prima Donna" when everyone sings "Light up the stage." you can see some actors and actresses singing the word "light" but you don't actually hear it until a few seconds later.
Continuity mistake: When Christine approaches her family mausoleum, behind her you can see an above-ground tomb that has chains around the top cover. There is something on top of the cover that looks like a bouquet of flowers covered in snow, and there is not a lot of snow on the tomb. Later, when Raoul and the Phantom are fighting and the Phantom slashes Raoul's arm. Raoul falls backward onto this same tomb, and when we see him from above, rising, the chains on his side are missing, and there is suddenly lots more snow all over the tomb. The bouqet (or whatever it is) is missing. However, in the next shot that shows the same tomb, now there is much less snow, the bouquet is back, and one-half of the side chains have reappeared. You can see the continuity by the tree at the head of the tomb, and the triangular wreath laid at the head of the tomb.
Visible crew/equipment: When Raoul jumps down the hole into the mirror room, you see he is alone. Between when he jumps down, and the appearance of the phantom's reflection, if you slow down the movie you see a man in a gray shirt in the mirrors behind Raoul. He appears in at least three mirrors. Slow-mo is not essential but does help.
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.
Continuity mistake: When Christine is in the Phantom's lair for the second time, after the Phantom puts the veil on her head, the camera has a close up of him (during the lines 'an eternity of this before your eyes') and the back of Chirstine's head can be seen not wearing the veil. When the camera pans back to her, she is wearing the veil and removes it a little later.
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: During the scene where Meg is looking for Christine backstage, we see her pass Firmin and Andre. Behind her Raoul approaches the managers and they turn to greet him. In the next shot they are turned round flirting with the chorus girls, Raoul is nowhere to be seen, and Meg passes behind them again.
Continuity mistake: After "Think of Me", Meg is pushing through the crowd backstage, searching for Christine and she finally makes her way out of the crowd. Their actions repeat in a shot from a different angle. The next shot is a close up of Andre sharing a cigar with a woman and in the background, you can see Meg pushing through the crowd again, even though she already passed Andre.