Deliberate mistake: During the finale, the backround looks like a sunset and there is a big door in the back. Watch closely and all of a sudden from one camera angle to the next (it's right after the big puff of smoke), the background changes to an elaborate background of layers of hearts, the door is gone, and there are about 60 more extras onstage. During the DVD Baz explains that they filmed the scene with both backgrounds and it just so happened that the beginning was better with one and the end was better with the other, so they put the puff of smoke in there to distract the audience so that they wouldn't see the change.
Deliberate mistake: When Satine and Christian are singing "The Elephant Love Medley" and Satine dismisses Christian singing "I'll drink all the time" and then heads down to the heart window of the Red Room. If you watch the chains attached to the elephant's head just after Satine passes under them and before Christian leaves they move as if being struck by something. The actors actually were on safety wires and Satine's hit the chains when she went in. They later edited out the wires so now the chains look as if they were hit by an invisible object.