Corrected entry: When Kai pulls Jack off the wall during the fight, Jack falls head first; when the shot changes to Jack landing, you can see him rolling backwards into position.
Corrected entry: When Kim joins the Wasabi dojo, she should not have kept her black belt rank; unless the schools are teaching the exact same style of martial art, her rank would not be recognized and she would have to start as a white belt again.
Correction: Not necessarily. If a school wishes, they can test your level of skill against theirs and decide where to start you with their training. When I switched from an Okinawan style to a Japanese style, I was tested and promoted a rank.
Correction: Momentum would have caused Jack to rock slightly forward on his landing thus making him roll backwards after hitting the peak height. In other words, Jack would have rolled forward and then backwards.