Visible crew/equipment: When Kim is talking to Joan the security guard, a crew member drinking a cup of coffee can be seen in the dojo.
Factual error: Jack enters the tournament as a recognized white belt but he is scheduled to face Kim who is ranked as a black belt. Tournaments do not allow match ups between white and black belts; it's forbidden in all styles of martial arts.
Continuity mistake: The ninja with the tattoo that attacks Jack is a large built man with olive skin. When Jack sees the tattoo on Kai's teammate, he is now a slight built, Caucasian teenager.
Continuity mistake: The kids fall to the ground after they are eliminated from the game but when Jerry takes out a knight and the wizard along the path, only the knight is seen lying down in the subsequent shots; the wizard is nowhere to be seen.
Answer: If you noticed, Kim was not sitting with the Black Dragons, so it's safe to assume that she didn't approve of their bullying tactics. She also flashed Jack a smile during the fight, so it's pretty obvious she had no interest in getting involved.