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.
Other mistake: Ethan kills one of the survivors. Sawyer thinks it's Steve but Hurley corrects him and tells him that it was actually Scott. They make a point of Scott being the deceased and Steve being the one people mix him up with. According to the actors playing Scott and Steve it was in fact Steve who got killed but the producers messed it up.