Continuity mistake: In season 2, episode 5, Jin and Mr. Eko are searching for Michael. Jin gets attacked by a boar and rolls down a hill to find the corpse of Goodwin. In this scene they are in the middle of the jungle. Two epiosdes later ("The Other 48 Days"), when Ana-Lucia confronts Goodwin they are on top of a mountain without trees surrounding them. This is confirmed in Juliets flashbacks in later seasons when Ben takes her to see Goodwins body.
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.