Continuity mistake: When JB dreams about singing "Master Exploder" in the small bar, he points at one guy in the audience and literally blows his mind. When he starts pointing you can not only see JB's face, but also how his elbow is in a slight angle. In the next shot the camera shows the guy JB is pointing at and his elbow is completely stretched. The views change several times and the angle of his elbow changes after every cut, until the guy's brain is finally blown out.
Continuity mistake: When all of the dancers are preparing for the showcase dance, Nora walks in with hair that has her usual bounce. When she and Lucy are talking in front of the mirror, her hair is almost completely straight, sporting just a few slight waves. When Tyler approaches her backstage, her hair is extra curly. It has only been a few minutes, and there was not enough time for her to have curled it. This is confirmed in the commentary.
Continuity mistake: At the beginning, when Benny G is sitting in his car listening to the remake of his song "I Cry" on the radio, in the exterior shot of the car there is a massive amount of water on the window. But, in the interior shot, there is not as much water on the window anymore, and there was no time between shots to put the windscreen wipers on.
Continuity mistake: When Mr. Dulaine forces Rock and LaRhette to dance the waltz together, he takes off his necktie and blindfolds LaRhette with it. Throughout the scene the blindfold is different nearly every time the camera angle changes - the "tail" created by the wide end of the tie gets longer and shorter, the knot alternately loosens and tightens and moves from side to side across the back of her head, and the whole thing slides up and down her nose. It's so distracting I spent the whole scene watching to see how it was going to move next.