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)
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.
Other mistake: In the dojo, one student is instructed to give 60 pushups on his knuckles. He goes to the side of the ring and starts them slowly while the small match starts between two other students. By the time Kreese talks to Miyagi only seconds later after the short match, the kid doing pushups on the side is completely gone although not enough time went by for that many pushups.