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.
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.
Gabby's Gold - S3-E8
Revealing mistake: When Kim and Gabby swing from the bar to kick the two villains, its obvious that Gabby kicked the guy in the knees, but he falls holding his chest. Plus Kim was a good 8-12 inches from her target and he fell anyway.
Visible crew/equipment: During the race, cameras can be seen on Kim's helmet.
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.