Continuity mistake: Season 6, episode 7 "Dr. Linus": When Ben writes 'ELBA' on the blackboard, he underlines it with a curved line, but as he walks to the back of the classroom in the next shot, you can see over his shoulder that the line is now straight. The handwriting of the letters has also changed noticeably.
Revealing mistake: When Desmond moves the rock, Smoke-Locke and Jack fight outside the cave while an earthquake shatters everything. Watch the leaves around and you'll notice that they don't move at all, giving away the camera effect. This also happens later on when Hugo, Ben and Jack are about to fix the cave of light.
Continuity mistake: As Locke stabs Jack's neck in their final battle, the wound is visible, above the neck line of his shirt. Once the rain stops and Jack speaks of his plan and kisses Kate, the wound is missing for the entire scene. The wound reappears on his neck during Jack's scene with Hurley and Ben at the cave opening. During the final sequence as Jack lies down and closes his eyes, the wound is visible in most shots, but in the final two wide shots, the dry blood make-up appears to be coming off and once again there is no neck wound.
Audio problem: When Desmond, Locke and Jack are standing outside the cave with light, Desmond says "maybe I can find a way out for you too," or something like that. Jack replies, "there are no do-overs." The camera then goes to over Jack's right shoulder as he says, "I tried that once." However, the words don't match what his mouth is saying.
Continuity mistake: Season 6, episode 8 "The Package": When Charles Widmore hands Jin the camera and tells him to turn it on, the lens is already out, therefore the camera is already on. When the shot cuts away you can hear him turning the camera on and the motor extending the lens.