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.
Homecoming - S1-E15
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.
Other mistake: When Jack and Rose talk the second time on the beach, they talk while it is cloudy and overcast. However, as Jack stands up to leave, he is brightly illuminated by sunshine.
House of the Rising Sun - S1-E6
Other mistake: When Walt says to his dad that his mum never talks about him, something briefly blows into shot at the top of the screen. There is no logical explanation for this as they are walking by the water, under no cover and nothing is around. (00:18:50)
Answer: He was eating a peice of an orange with the skin still on.
XIII