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).