Revealing mistake: When Daniel is running from Johnny and his gang after the bathroom incident at the dance, there's a lot of fog outside. If you look at one of the trees in the background, you can see that all the fog is being puffed out from behind the tree - obviously a fog machine.
Revealing mistake: When Daniel is about to paint the fence of Mr. Miyagi, Mr. Miyagi tries to catch a fly with chopsticks. Daniel tries as well. You can see that this "fly" is attached to a wire or a nylon string, moving like a pendulum and bounces as if someone's pulling the string.
Revealing mistake: In the beginning where Daniel and his mom finally arrive at the new apartment, pay close attention to the wooden entry fence. Soon after Daniel's mother states, "This is the Garden of Eden," you can see Daniel's soon-to-be friend "Freddy" lining himself up behind the wooden fence prior to Daniel's mom opening the door.
Revealing mistake: When Mr Miyagi saves Daniel from Johnny, you can see that it's not Pat Morita jumping over the chain fence, but his stunt double (Fumio Demura). (00:39:10)
Revealing mistake: When Mr. Miyagi beats the Cobra Kai guys dressed like skeletons you can see the stunt double (Fumio Demura) doing it for him.
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.