Continuity mistake: In the final fight between Daniel and Johnny, there is a time when Johnny's head band falls off (after Johnny scores his second point). Right after it falls off, if you look quickly you can see it back on, then it goes back off. (02:00:50)
Suggested correction: That right unless there were a few bits of the scene cut where the referee gave it back to him.
Continuity mistake: Before the dance in Mr. Miyagi's work area you can see the red shower curtain with the polka-dots that Danny wears to the dance hanging on the wall. After the dance, when Danny is in the work area after getting saved from the Skeletons, you can still see the shower curtain on the back wall.
Suggested correction: The mistake assumes Mr Miyagi only had one shower curtain. Many people have more than one to replace the current one when it's worn or so dirty with soap scum they are cheaper to replace than try to clean.
Continuity mistake: When Mr. Miyagi saves Daniel from the Kobra Kai during the night of the Halloween dance, Mr. Miyagi flips Johnny to the ground and only strikes him in the stomach. The next morning, when Daniel and Mr. Miyagi go to Kreese's dojo, Johnny is seen with a black eye. Very hard to get one since he was never hit in the face.
Suggested correction: When Miyagi dropped him, the black eye could very well be from a bump in the ground or a rock.
From the way Johnny was flipped, he landed on his back; unlikely he could have injured his eye.
Revealing mistake: In the final match between Daniel and Johnny, you can see Daniel covertly tap his left leg (the bad one) so that Johnny knows which knee to grab to hurt him.
Suggested correction: I just rewatched this moment and see that Daniel is instinctively tapping his sore leg, with the bandage there, not sending Johnny any private signal.
Other mistake: After Tommy's arm gets broken during the skeleton fight with Miyagi he appears days later in practice drill in Kreese's dojo, with his right arm in a sling. Huffing punches like the other Cobras, which would be impossible with his injury. (00:49:45 - 00:50:45)
Suggested correction: Tommy is only punching with his good arm, which is possible. The twisting of his hips makes it appear he is using both arms.
Other mistake: In the semi final match between Johnny and Duval his name is listed behind them on the board as Vidal. But you can hear him being announced as Duval.
Suggested correction: He doesn't say "Duval", he says "Darryl Vidal." While the character isn't listed by name in the credits, only listed as "Karate Semi-finalist", he was in fact played by Darryl Vidal, who was an actual black belt at the time of the movie.
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.
Suggested correction: Although this observation is accurate, keep in mind that the Cobras have a reputation as dirty and vicious fighters so it is very possible their earlier opponents were intimidated by them and therefore easily beaten.