Continuity mistake: When Miles is sent to deliver "The Package" (i.e. the dead body) to Dr. Chang, after the body is taken out of the van, Miles is seen closing the door to the back of the van. After a return from a flash forward and back to 1977, the door to the back of the van is open again.
Continuity mistake: Season 6, episode 8 "The Package": When Charles Widmore hands Jin the camera and tells him to turn it on, the lens is already out, therefore the camera is already on. When the shot cuts away you can hear him turning the camera on and the motor extending the lens.
Live Together, Die Alone, Part 2 - S2-E24
Continuity mistake: Penny's letter to Desmond changes as he reads it. The text stays the same, but the handwriting and position of the words on the page change between the two shots where you can see the letter from the front. Also, for the audience the letter is read aloud with Penny's voice. Interesting is the fact that there is one sentence omitted: "Sorry to be so dramatic, but these are dramatic times, are they not?" (You can read this sentence in both "versions" of the letter though).
Live Together, Die Alone, Part 2 - S2-E24
Continuity mistake: As they are walking through the jungle, Sawyer goes to pick up a doll. He reaches down and nearly touches the doll. But in the next shot Kate grabs his arm, to stop him, before he even bends over. (00:18:00)
Collision (a.k.a.Old Habits) - S2-E8
Continuity mistake: In the jungle while Sayid is tied up, when they are told to leave, Jin's handcuff is higher on his wrist. As he walks past Sayid the handcuff is so low around his hand that it would slip off easily. (00:26:45)
Continuity mistake: When we first see young Jacob holding the white stone with his brother, the stone he has changes shape from long and rectangular to square.
Ab Aeterno - S6-E9
Continuity mistake: Season 6, episode 9 "Ab Aeterno": When Jacob pulls Richard upright after dunking him, his hair flies back over his head, leaving his face fully visible. The shot changes to a front view and Richard's hair is now covering most of his face.
Continuity mistake: When Sawyer dumps out the water canteen Juliet tosses him, his hand moves from the top of the base to the bottom, and the angle at which he pours the contents out changes, as well. (00:24:15)
Answer: He was eating a peice of an orange with the skin still on.
XIII