Factual error: It says that Jerry is running a judo dojo, but when Jack walks in Jerry is teaching his students to punch - judo doesn't use punches.
Continuity mistake: The lockers in the Bobby Wasabi dojo change from blue to green in the same episode.
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.