The End (2) - S6-E18
Continuity mistake: As Locke stabs Jack's neck in their final battle, the wound is visible, above the neck line of his shirt. Once the rain stops and Jack speaks of his plan and kisses Kate, the wound is missing for the entire scene. The wound reappears on his neck during Jack's scene with Hurley and Ben at the cave opening. During the final sequence as Jack lies down and closes his eyes, the wound is visible in most shots, but in the final two wide shots, the dry blood make-up appears to be coming off and once again there is no neck wound.
Continuity mistake: At the end, when we see Ben lighting a candle with a matchstick in the cathedral during the entering of Eloise, he puts out the matchstick so we see that the flame is gone. In the next shot, the flame is back and Ben is doing exactly the same thing, but we see it from another view.
Continuity mistake: Ses. 5, ep. 5, "This Place is Death". When Daniel is telling Charlotte that he has a plan, and explains, "When we were back at the hatch, I talked to Desmond", he places his left hand on top of his right, holding Charlotte's hand between them (seen at bottom of the screen). When the angle changes to a shot above his shoulder, his left hand is suddenly back under Charlotte's head, with no time to move between shots. (00:32:50)
Continuity mistake: In the very beginning of the pilot episode, Jack runs out of the jungle. He looks around and hears distant screams. While he is looking around, you can see through the bushes that there is nothing but beach on the other side. But when he turns around, the entire beach just on the other side of that bush is filled with wreckage. The wreckage would have been visible from the other side of the bush had it been there.

Other mistake: In the scene with Sawyer and Michael drifting on the pontoon, where Michael is crying, you briefly see a boat with a mast in the background in one shot over Sawyer's right shoulder as he faces the screen, just before he says "Are you all right Mike?". (00:38:10)
Continuity mistake: 6-01-02 - LAX: When Sayid is drownd and laid on a carpet, his head swaps from being by the edge of it almost out, to several inches inside the carpet.
Continuity mistake: "The Variable": When Faraday is on about the variables, he has his jotter in his hands. Camera does a quick cut and it's now on the floor.
Continuity mistake: When Miles and Hurley deliver The Package, the way it's held is constantly changing.

Continuity mistake: The blood on Juliette's mask changes drastically between shots. (00:08:15)
Ab Aeterno - S6-E9
Factual error: Season 6, episode 9 "Ab Aeterno": The episode is supposed to take place in the Canary Islands, Spain. However all the characters speak with either Mexican, Puerto Rican, or Cuban accents. In the 19th century there wasn't such a blend of American cultures.

Through The Looking Glass (2) - S3-E23
Continuity mistake: When Jack hands the walkie-talkie to Ben, the way he holds it differs between the two angles. In one angle, he is gripping it; in the other, he is holding it on his flat palm. (00:10:30)

Continuity mistake: Just after the title sequence, we see Faraday holding a map in two hands in a close-up, but with one hand and one hand pointing at the map in a longer shot. (00:10:40)

Continuity mistake: At the very start, when Ecko and Yemi break into the shed, the hand holding the packet of biscuits on Yemi changes between shots. (00:01:30)

Continuity mistake: When Sawyer is in prison, he gets a visitor who takes something out of her bag. As she does so, Sawyer has his arms crossed in one shot and outstretched in the next. (00:19:20)

Continuity mistake: When Sayid is talking about moving the boat, Sun's hair is blowing in the wind in one shot but nice and neat in the next. (00:03:00)

Continuity mistake: When Sayid finds all the passports, he opens one and the way he holds it differs between camera angles. (00:25:00)

Continuity mistake: When Sayid sits down in the café, the woman he sits opposite is playing with her hair in the shot facing Sayid, but has her arm down in the shot facing herself. (00:06:33)

Character mistake: When Jack and co find Frank, we see Jack checking for a pulse and declaring there is one. However, Jack is using his thumb to check for a pulse on Frank's wrist. As a doctor, Jack would know your thumb has its own pulse. (00:33:40)

Continuity mistake: In Tunisia, we see someone grab a newspaper and hold it by the side and top in a long shot, but from opposite sides in the close-up shot. (00:22:10)

The Beginning of the End - S4-E1
Visible crew/equipment: When Hurley hugs the detective after being told he can go to the mental hospital, a camera and operator's hand can be seen in the background. (00:06:00)
Answer: He was eating a peice of an orange with the skin still on.
XIII