Revealing mistake: After Sawyer has been shot with the syringe thing (I'm not sure if Kate had been shot yet) Jack fires his gun five or six times into the jungle. The last few times he fires it there is no flash or any indication that the gun has been fired.
Continuity mistake: Penny's letter to Desmond changes as he reads it. The text stays the same, but the handwriting and position of the words on the page change between the two shots where you can see the letter from the front. Also, for the audience the letter is read aloud with Penny's voice. Interesting is the fact that there is one sentence omitted: "Sorry to be so dramatic, but these are dramatic times, are they not?" (You can read this sentence in both "versions" of the letter though).