Continuity mistake: Just before Locke, Kate, Charlie and Jack head off to the cave for water, the strap on Charlie's holdall flips without anyone touching it. Note the metal clip on the strap that is visible in the first shot and not in the second. (00:02:50)
Continuity mistake: When Locke and Mr. Eko watch the Orientation video in the pearl station Dr Chang has both arms and the screens behind him show people working in the swan hatch. His arm was badly damaged in the incident before the swan hatch was built and he should.have had a prosthetic arm when the pearl video was made.