Continuity mistake: We first see from the inside of the door (and therefore backwards) the instructions that Mr. Miyagi leaves for Daniel to paint the house. In the next shot we see the same note from the outside - from Daniel's viewpoint. Clearly they are two different notes. The left & right arrows switch directions, the drawings of the hands change, the position of Miyagi's signature changes, and the placement of some of the exclamation points changes.
Continuity mistake: When the Rad Pack first meets and are skiing together, Dan O'Callahan is wearing a blue baseball cap and sunglasses. In some later shots he is wearing a stocking cap and goggles. (00:31:25 - 00:32:00)
Continuity mistake: At the beginning of the film, the young Roy breaks a board of the hen-house wall with a pitch. When the shot cuts back to the hen-house wall a moment later, the hole is a different shape and in a different place.