Continuity mistake: In the flashback scene (where Cassie has the crazy long hair) we see "young" Cassie perform a routine in the studio. Zach comes out of the shower towelling his hair and watches her. We see his hair is messed up having just been roughly dried with a towel. The next shot is Cassie dancing, then the next shot is back to Zach, and this time his hair is combed nicely down.
Deliberate mistake: During the finale of "One," near the end of the number when the entire cast and all of the extras, dressed in gold lame tuxedos, are doing the last kick line before the credits, one of the dancers (second row, third from the right) falls down and gets right back up again. While this mistake wasn't "deliberate" as such, it was probably simply prohibitive to film the entire kick line over again for the sake of the one fall that is barely noticeable, so was deliberately left in.