Revealing mistake: Kim is supposed to be hanging from the tree by the ropes around her wrists, but you can see she is standing on a platform.
Continuity mistake: The Bobby Wasabi dojo receives the amazing Punch Master Elite that is apparently not even available in stores yet, however you can see the piece of equipment in a previous episode, S2E15: A Slip Down Memory Lane. The Punch Master Elite can be spotted in the back left corner of the dojo in the first scene. Other than that you can just barely see it if you look closely into the dojo when the camera goes to that angle in the scene where Jack regains his memory and breaks the under 15 record for brick breaking. Aside from these 2 sightings, you don't see it again because it is a flashback episode, and beyond that, you actually don't see it again until S2E20 when Milton opens it as a gift from the Mayor, awarded for tremendous bravery in capturing an escaped convict.
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.