Continuity mistake: When Jack is talking to Kim after he defeats the impostor, in one shot you can see the actor who played the impostor appear over Jack's shoulder; he's just standing there watching the rest of the scene.
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.