Continuity mistake: When Satine is singing "One day I'll fly away", Christian climbs up the elephant and encounters her. He leans on a column with a red ball. The ball keeps moving between shots, even though Christian keeps still in the same position, watching Satine. Sometimes the ball is down, sometimes up, sometimes close to him.
Continuity mistake: In the final scene, when they are performing the play before the audience, watch as Satine makes her initial appearance and rises up out of the floor. In some shots, you can see her leg sticking out through the slit in her dress, in other shots, her leg is still inside her dress.
Visible crew/equipment: When Satine is singing 'One day I'll fly away,' she goes up the steps to the top of the elephant. If you look to the top windows of the building behind her, you can see a strange shape gliding past the lit windows from left to right. I'm not sure what it is, since it isn't the shape of a person and it looks like it's on a track. Then when Satine sings, 'Why live life from dream to dream?' the shape goes back from right to left, and at the last second, before it cuts to Christian, the lights go out. Now, I've seen the behind-the-scenes of footage of Moulin Rouge, and that scene was probably behind a blue screen so I haven't a clue what the shape is.
Continuity mistake: When Christian knocks over the candle in the Red Room, the flame goes out and there is another shot of it out. Then suddenly there is a shot of the candle knocked over but still burning on the table and it's reflected in some of the silverware. Then the next shot of the table, the candle is suddenly out again.
Continuity mistake: During the end of One Day I'll Fly Away, Satine intended to sit on top of the elephant room. When she was still standing, part of her hair was in front of her left shoulder. However when she sat and sang "Fly, fly, away" (the next shot) none of her hair was in front of the shoulder.
Continuity mistake: During the "Rhythm of the Night" dance sequence you see The Petite Princess singing on the bar in a hindu outfit behind the gnarly men. After that you see her in her can can skirt. Then any time you see the gnarly men she's back in the hindu outfit.
Continuity mistake: In the end of "Your Song" when Satine and Christian return to the Elephant Room, Satine puts her right arm around Christian's neck. Shots from Satine's right side reveal her right forearm (you can see her elbow), but shots from her left side show that her sleeve cover the entire forearm, and uncover it when she doesn't put her arm in Christian's neck anymore (touch his shoulder).