The length of the chain that links the handcuffs originally worn by Kate becomes much longer when used on Jin.
When Jin is washing his hands in his house after beating someone (before Sun slaps him), his right sleeve is bloody, but then the camera returns to his right side and the sleeve is clean.
When Jin attacks Michael, the watch Michael is wearing disappears when the camera switches between close ups and far shots.
When Sun visits Michael while he's chopping wood, he is wearing a gold watch on his right wrist. For one brief moment, the watch is in his hand circled around his fingers, then the watch is back on his wrist just before he takes it off to give to Sun.
After Michael first says "You speak English?" to Sun, he is holding the axe with his left hand and holding up his right hand. After the camera switches angles, he is holding up his left hand and drops the axe with his right hand.
The Korean couple share the same last name. In Korea, women do not take the last name of their husbands upon marriage.
When Jack brings survivors back from the beach and goes to refill his water bottle, his tattoo is on his right arm, when it should be on his left arm. Possibly the scene was 'flipped'.
Near the end, when Kate is sitting alone on the beach, and Jack comes up to talk to her about moving into the caves, you can see vehicle tire tracks in the sand.