Continuity mistake: When Satine is dancing with Christian in the first Moulin Rouge scene, her pink feather dress's straps are very thin. But when Chocolat sets her down backstage after she has fainted, her straps are much thicker and are more intricate. This is mentioned on the DVD - the later scene was filmed first, and changes had to be made to the dress in order for Nicole Kidman to dance around in it. (00:19:40 - 00:21:30)
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.
Continuity mistake: In the 'Come What May' sequence in the theater, in some shots, after Nini tells the Duke about Satine and Christian, the other dancers are sitting in chairs and there is a giant pile of chairs that the stage crew is setting up. But when the Duke says he doesn't like the ending, there are no chairs, no dancers, and no stage crew.