Other mistake: The Monster appearing in the pilot and causing the turbine to explode is a mistake (not trivia). This is actually an artefact of poor CGI effects that was left in the show in error. It was confirmed by the producers. You can see it best here: http://www.lostpedia.com/wiki/Image:Turbine_Explosion.gif.
Ocean Alert - S1-E10
Other mistake: Right before Nikki gets captured, the Rangers are blasted by the monster, causing big explosions right in front of her, but somehow she doesn't even notice this.
Other mistake: McKay and Jackson enters a room and runs into 2 armored figures, Jackson eventually reveals that they are empty suits, however in every shot shot from behind the suits, the suits are constantly moving, as if they are hanging on strings.