Continuity mistake: When Mike Barnes walks into Mr Miyagi's back garden where Daniel is training, they fight and Terry Silver appears. When Terry puts his book to Mike's face, in the first shot it's on the right side of Mike's face, but next shot on his left, then back on his left.
Continuity mistake: When Daniel is being beaten up by Mike Barnes in the Bonsai store, just after Daniel breaks the glass in the window, look to the left of the screen. There are 4 crates, 1 on top of each other, then when Mike throws Daniel away after punching him, look in the background there are 3 crates and then two next to the 3 crates piled up instead of 4, like we saw in the previous shot.
Continuity mistake: When Daniel and Jessica are about to climb back up the cliff face, they both tie the ropes to their harnesses with a knot at the end of the rope, yet when you see a shot from the top of the cliff face, you can see quite a lot of rope trailing behind Jessica which shouldn't be there.