Continuity mistake: At the end of the scene in the gym of the mental hospital when Hurley and Dave talk, in the background there is a guy sitting on the floor in a yoga-like position. His exact location changes between shots, as you can tell by the ground-lines. First he sits on the red line, next to where the blue and the yellow lines cross, then he sits about 5 feet further to the right, and finally he is back exactly on the same spot as in the beginning.
Continuity mistake: When Libby kisses Hurley at the cliff, there is a strand of Libby's hair which you can see hanging freely over her left cheek when the camera is on Hurley. When the camera is on Libby you see the same strand pinched between their heads. Then as the camera switches back on Hurley the strand hangs freely again. It's not possible that this happened only through the force of wind as their heads are stuck together quite tightly throughout the whole kiss.