Continuity mistake: In the first shot of Locke sitting in the wheelchair, in the airport lounge, he sits alone directly in front of the long rows of chairs. However, in the next overhead shot, the airline steward is at Locke's side as he sits near the large windows, nowhere near the chairs.
Continuity mistake: In the Oceanic Int'l departure lounge, Locke sits in his wheelchair near the large window, with the doomed plane in the distance. The attendant's desk is on the left, but the black lounge chairs, which are normally situated toward the center of the lounge, are gone in this shot; the chairs at the end of each row should be visible at this angle. These chairs are also seen when Hurley crashes the scooter into them.
Continuity mistake: When Michael sits with Walt at the airport, Michael says, "If you're worried about Vincent," and the newspaper in his hands is folded and held straight up with the blue Oceanic envelope. Yet, when he says, "Dogs fly in the luggage compartment all the time," the newspaper is sideways and there is no blue envelope.
Continuity mistake: When Kate and Sawyer begin their swim, Kate is not wearing a bracelet on either wrist, as she heads into the water. In a few following shots, including when Sawyer goes to "See what they got on em," Kate wears a bracelet on her right wrist, but when they head down to retrieve the case, the bracelet is gone as she pulls on the case. After Sawyer frees the case, in Kate's close-up the bracelet reappears, but now it's on her left wrist, yet when they reach the surface the bracelet's on her right wrist. Whew!
Revealing mistake: Season 3, episode 1, "A Tale of Two Cities.": In the scene where Ben/Henry is presenting a breakfast table to Kate, he mentions coffee which we can see is in a French press. Ben/Henry "finishes" the coffee by pushing down on the plunger of the french press, but uses only one finger with barely any pressure. In reality, a french press takes a significant amount of pressure to get the plunger from top to bottom, more than could be generated by just one finger. Additionally, we can see that the mesh-screen component of the French press stays at the top, rather than plunging down, which it should in order to filter out the grounds.
Plot hole: Sawyer pulls the bullet out with his bare hands, we are led to believe, through the cut the bullet made. When you are shot, the flesh immediately seals up, meaning you would need a knife or something like that to get it out. Sawyer only had the gun, as he could not have hidden the knife AND the gun.