Continuity mistake: In the very beginning, when Daniel and his mom start to drive away from their old house in New Jersey, Daniel's bike is strapped to the roof of the station wagon. The bike is positioned with the front tire of the bike facing the back of the vehicle. A couple seconds later, in the very next cut scene, the bike is facing the opposite direction.
Other mistake: The end tournament is supposed to be only the very best trained fighters in brown and black belts. Yet the majority of opponents against the Cobras are easily defeated, with weak tactics, unlike Daniel-san and the Asian guy, who actually use fight techniques.
Continuity mistake: When Mr. Myagi and Daniel go to the dojo to stop the fighting, the earlier scene revealed that they left the apartment at 10am. Assuming that there was some time to get to the dojo, they left a few minutes later and then drove to Mr. Myagi's house to start the training. Daniel starts to wax the cars and the sky is showing a sunset. At the latest, it may have been around 11am when they got to the house, so there is no way the sun could be setting.