Factual error: Naomi Doret, the woman who parachuted onto the island, is explaining about the outside world finding the wreckage of flight 815 "off the coast of Bali, in an ocean trench 4 miles deep". The problem with that statement is that Bali is nowhere near the Pacific Ocean, it's in the Indian Ocean. Oceanic flight 815 was a direct flight from Sydney, Australia to Los Angeles, US. That flight wouldn't go anywhere near the Indian Ocean or Bali.
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.
Continuity mistake: When Jack is packing water bottles in to the sack and Locke says "I think one of us should stay and help Charlie salvage the wreckage", you see Jack putting a bottle in to the sack. His hands are now empty, but when it cuts he suddenly has a new bottle in his hand which he puts in to the sack.
Visible crew/equipment: As the "rescue" boat nears the raft with Jin, Sawyer, Michael and Walt, it has a spotlight shining on the four aboard the raft. That spotlight is the only light source in the area, yet the boat is bathed in bright light from behind, which also reflects in the boat's pole.
Visible crew/equipment: When Sawyer finds his blue tarp that the boar ran off with earlier, Sawyer hears the whispers, then the boar reappears and chases him. When the mean old boar flips Sawyer over, the chain link fence (used for the stunt) is clearly visible beyond the grass, at the top right corner of the screen. (Also seen on Disc 7.)
Revealing mistake: After Sawyer jumps into the water to retrieve the rudder, Michael tosses him the rope then shouts, "Tie it around the rudder and we'll pull you in." Three shots later, in Sawyer's close-ups, mountains are visible at the right of the screen, whereas in the previous and following consecutive shots they are surrounded only by water at this point in time.
Continuity mistake: After Sawyer admits to Kate that he doesn't have the inhalers, Sayid and he get into a tussle. In the first shot, the back of Sayid's white shirt is fairly clean as he is standing, but in the next wider shot the back is completely filthy - before he and Sawyer ever even hit the ground.
Revealing mistake: When Sayid, Kate, Sawyer and the others make camp for the night, on their way back from hearing the French woman's transmission, they sit around the fire talking. Sawyer has a cut over his right eye, but in every other close-up of Sawyer the cut is over his left eye. The shots are flipped.
Continuity mistake: Just before Michael says "You're going to pull the bullet out with your bare hands?", Sawyer's hair is very wet and pulled back, as if it were in a pony tail. When the camera switches back to Sawyer saying "You got a better idea?" his hair is a lot drier and covering his face. In the next shot, it is pulled back again.
Continuity mistake: In the scene where Sawyer collapses from his bullet wound, he collapses onto his knees and then twists so that his good arm is towards the ground. From there, he rolls to his back. Then the camera angle changes so we're looking at Michael and Jin running towards Sawyer from the front. Sawyer is now on his good arm's side.