Continuity mistake: When Kate finds the pilot's wingpin in the mud, the pilot's reflection is seen in the water as he lies on the branches above Kate. When Jack approaches they all look up and in the overhead shot the pilot's position differs and he lies on different parts of the branches, note their shape.
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.
Continuity mistake: When Charlie, Kate and Jack are in the nose wreckage, to find the transceiver, there is a shot in first class, facing the cockpit, showing the glass wall with the decorative circular design. When Charlie is aboard the flight, running from the stewards, he stands beside that glass wall, and the circular pattern is reversed. Neither shot is flipped.Super Grover
Continuity mistake: When Jack drops to his knees, after removing the undershirt, one white shirt lies stretched out horizontally on the ground directly in front of him, with both knees centered in front of it; the other shirt is off to his right (viewer's left), with the undershirt he drops. Three shots later, still on his knees, all three shirts lie rumpled to his right; eleven shots later, the single white shirt once again lies horizontally directly in front of him, in the very same position as the earlier shot.Super Grover
Continuity mistake: When Charlie leaves his seat on the airplane, as he is followed by the stewards, he walks through economy (blue stripe seats), then walks through business class (grey stripe seats and roomier) - where Boone and Shannon sit. But, in Charlie's next close-up, when the plane shakes, he leans on the blue seat in front of him, which he already passed and is farther back in the plane's cabin.Super Grover
Continuity mistake: In the very beginning of the pilot episode, Jack runs out of the jungle. He looks around and hears distant screams. While he is looking around, you can see through the bushes that there is nothing but beach on the other side. But when he turns around, the entire beach just on the other side of that bush is filled with wreckage. The wreckage would have been visible from the other side of the bush had it been there.