When Pennys voice-over reads Desmonds letter when he's suicidal after Kelvin's death, she misses out a sentence (probably just done for flow of script), but in the next scene, the layout of the letter has changed - the missed out sentence is in a different position on the letter.
When you see the sailboat in the distance, the bow is facing inland (toward the beach). As they swim up and get on the boat, it is still heading that direction. Shots from the boat have it facing out to sea.
When Jack, Sayid and Sawyer board the "Elizabeth," Hume fires several rounds through the hatch. They find him cradling a semi-automatic shotgun, probably 12-gauge. But the holes in the hatch are too small for buckshot and too large for slugs.
When Michael opens the flare gun to examine the flare, the primer cap has a dent in it, showing that it has already been fired; moments later he fires the same flare to illuminate the boat from 'The Others'.
The goof item below may give away important plot points.
When the bird swoops down on the rescue party, Michael tries to shoot it with a Glock pistol that turns out to be empty. The pistol "clicks empty" several times. The way a Glock pistol works, it will click once and only once when empty and "in battery."