Continuity mistake: When Claire is holding Aaron talking to Locke, she says "I can't believe he is still sleeping" and they show him sleeping. She then asks Locke if he wants to hold him and then hands Aaron to Locke. His eyes are wide open. Then you see Locke obviously holding a doll in the next shot and they are talking about him still being asleep. Locke then hands Aaron to Charlie and the eyes are again wide open and they are still talking about him being asleep.
Revealing mistake: As several camera angles show, Sawyer's makeshift stretcher was made by drilling multiple holes in the upper frame struts, through which was threaded rope made from dried roots or vines. The cast who supposedly constructed it were not carrying power drills among their primitive implements.
Continuity mistake: In the scene where Sawyer collapses from his bullet wound, he collapses onto his knees and then twists so that his good arm is towards the ground. From there, he rolls to his back. Then the camera angle changes so we're looking at Michael and Jin running towards Sawyer from the front. Sawyer is now on his good arm's side.