Continuity mistake: When Claire finds out she is pregnant, her hair is either messy or neat depending on the camera angle. This is most noticeable when Thomas says it could be the best thing ever. (00:07:35)
Continuity mistake: When Jack and Claire open the music box, from the back angles their heads are almost touching each other, but from the front angles it's noticeable that both guys are sitting wider apart.
Continuity mistake: After the submarine sinks, Jack is in the beach hugging Kate and a strand of wet hair is on his forehead. When the angle changes the hairstyle has changed and his forehead appears clear.
Continuity mistake: When the Smoke smashes the armed guard against the cage he lies unconscious with his left arm stretched out. A frame later, from another angle, the arm rests by his side.
Continuity mistake: When Robert and Danielle banter about what the name of their baby will be, Robert has Danielle's face cupped in one hand, and then suddenly in both hands. (00:06:10)
Continuity mistake: When Libby kisses Hurley at the cliff, there is a strand of Libby's hair which you can see hanging freely over her left cheek when the camera is on Hurley. When the camera is on Libby you see the same strand pinched between their heads. Then as the camera switches back on Hurley the strand hangs freely again. It's not possible that this happened only through the force of wind as their heads are stuck together quite tightly throughout the whole kiss.
Continuity mistake: In the first minute of the episode when Sayid finds the wire on the beach, his left pant leg is not torn. When he follows the wire into the jungle, just before he trips Danielle's trap, the left leg of his pants is already torn, in exactly the place where the branch will stab him. (00:02:50)
Factual error: This is across the whole show, but made perfectly clear in the episode "The Whole Truth" (Season 2). Korean women do not change their last names upon marriage. A woman in Korea cannot be identified by name as someone's wife. And they would never be addressed that way. But Sun's fertility doctor addresses her as "Mrs. Kwon". Korean women can adopt their husband's family name if they move to a country where that is commonplace, but Sun was still in Korea at this point, and even after they crashed on the island, she had only just left the country.
Through The Looking Glass (1) - S3-E22
Continuity mistake: On the plane, Jack's paper is on the armrests until he notices the article; at which point, it is now on the seat next to him. Pay attention to the black marker on the seat. The amount visible changes. (00:02:10)
Continuity mistake: Alex gets handed her gun while she has bloody hands. She then proceeds to run to her boyfriend in the woods. When she arrived, her hands are clean. (00:19:00)
The Man Behind the Curtain - S3-E20
Continuity mistake: When Sawyer gets back to the camp and is talking to Sayid, in the shots facing Sayid, Sawyer's hair is swept back but in the shots facing Sawyer it's hanging down his face. (00:09:30)
Continuity mistake: When Yemi is reaching out to the cross that Ecko is holding in the clearing, his hand/grip on the cross differs between camera angles. In one, for example, his pinky is curled up but out straight in the following shot. (00:36:30)
...And Found - S2-E5
Continuity mistake: When Jack calls Sun on the beach, there is no one near her. When the shot changes to a close-up, someone is walking past her. (00:07:40)
Audio problem: Goodwin states, "the hills are blocking it," referring to the radio signals. However, the audio is of Locke saying the line. (00:30:20)
Suggested correction: That's Brett Cullen's voice.
