Continuity mistake: In the scene where Sayid and Shannon are talking over the map and Shannon leaves, Sayid has his head resting against his hand with his fingers in his hair in the close up. When the shot changes his fingers are not in his hair, then when it changes back to a close up, they are again.
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.
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.