Continuity mistake: When Jack shows Locke the case with guns, the bar trim beneath the handle is whole and unbroken. However, in "Whatever the Case May Be" when Boone tries to open the case without the key, the trim beneath the handle breaks off and is damaged. (00:27:45)Super Grover
Other mistake: Ethan kills one of the survivors. Sawyer thinks it's Steve but Hurley corrects him and tells him that it was actually Scott. They make a point of Scott being the deceased and Steve being the one people mix him up with. According to the actors playing Scott and Steve it was in fact Steve who got killed but the producers messed it up.
Continuity mistake: When Jack shows Locke the suitcase full of guns, you can see a stick visible in Locke's right hand. However, when Jack asks if Locke knows how to use a gun, you can see that after the camera has panned around, Locke is now holding the gun with both hands, with the stick nowhere to be seen.