It cost $250,000 just to ship the wrecked plane pieces to Hawaii. The wreckage was clearly visible to aircraft landing at nearby Honolulu airport, so airlines were advised to tell concerned passengers that they were actually seeing a TV set.
The scene where Jack asks Kate to sew up his back injury was the audition scene used to select the two actors to play Jack and Kate.
Dominic Monaghan, Matthew Fox and Evangeline Lilly were not allowed to see the cockpit set before shooting. They were blindfolded until cameras rolled and their reaction to seeing the cockpit leaning against the trees was real. This one-take is what was used in the pilot episode.
Jack's speech about counting to 5 to face his fears was written well before Matthew Fox was cast in the role - who coincidentally has a large 5 tattooed on his shoulder.
The still-turning jet engine on the beach that sucks up one of the survivors was added in digitally later. During filming, all that was on set was the cowling; a stunt man who was pulled sideways was filmed separately, and digitally inserted into the live-action footage. Director J.J. Abrams later joked during a TED talk that without the advantage of digital effects, the only way to do that scene was by actually killing the stunt man.