Continuity mistake: When Sun and Jin sit at the table at the airport, both cups' lids are on properly, yet for the "spill shot" one lid is askew, and Sun's hand changes between shots to be in perfect position to knock the cup over. Things on the table instantly change positions, such as the clear plastic croissant container that jumps back onto the red tray. This applies to Exodus 2, as well.
Continuity mistake: When Walt notices the pillar of black smoke, in the overhead shot everyone gathers well behind the raft, including Claire, who was just sitting in front of the bushes in the previous shot. However, in the next shot, all the survivors are now gathered at the side of the raft.
Continuity mistake: When Jack and Ana-Lucia sit in the airport lounge she takes out her cell phone when it rings, and in this shot her glass is nearly full and has plenty of ice. Yet, when she leaves a moment later, the glass is nearly empty with no ice whatsoever.
Continuity mistake: When Danielle approaches the beach campsite, in his close-ups, Walt hides beside a tree and holds it with his left hand. However, in the shot between his close-ups, facing Danielle, Walt is hunched over with his hands leaning on his knees.
Revealing mistake: In the scene just after Sawyer is mounting the radar on the mast of the shop, Sayid hands Michael a flare gun. He opens it to show that there is just 1 shot left. If you look closely the flare gun shell has already been fired (notice the center fire pin is indented).