Factual error: At the end of the first semifinal, as Cheng's gang gather to congratulate him, the events are being recorded for posterity by a photographer standing about 6 feet away, who, unfortunately is using at least a 200mm lens. I'm not sure he could even get Cheng's left eye into focus.
Continuity mistake: Dre visits Han when he is smashing his car, and Han sits in the driver's seat; Dre sees the paper clip on the hood - the paper moves several times during the shots. From having a quite amount of glass on it, to no glass, to a little glass. And it switches positions three times.
Audio problem: When Dre is leaving Meiying's violin practice in the auditorium there is a long shot of her playing her violin showing her left side as Dre walks to the exit. The notes she is playing are vibrato - varying the pitch of the notes by rapidly pivoting the finger on the strings - but her hand is perfectly still. Even though you can only see part of her hand it is obviously that her playing style doesn't match the notes being played.
Factual error: When Dre and his mother leave Detroit for China, it is daytime, and the flight is 13 1/2 hours, then during the opening credits, night falls and then the sun comes up again. Since they were traveling west and time was going backwards through 12 time zones, there is no way it could have ever gotten dark. It would have been light the whole time.
Continuity mistake: In the scene where Master Li looks at his students bowing to Mr. Han, he is standing up in the crowd and a few moments later he is on the floor behind Mr. Han and Dre when they do their fist bump. In the alternate ending he was on the floor because he was beaten by Mr. Han in a battle, but in the original scene he just randomly appears on the ground.