Continuity mistake: When one of the stormtroopers unties Han Solo before he is put into the carbonite, watch his wardrobe - he has a disappearing / reappearing jacket on. This is fixed to an extent on the DVD - the jacket is now lightened to almost match his shirt, but it's still shiny like leather. (01:32:05)
Visible crew/equipment: This can only be seen in the widescreen version. When Han, Leia and Chewie venture out of the Falcon to investigate the cave they're hiding in on the asteroid, as they walk towards the left of the screen you can see the edge of the tarpaulin sheet they're standing on as well as the faint outline of a crew member trying to get out of the camera shot.
Continuity mistake: Near the end of the film, when the Millennium Falcon is trying to get away from Vader, there's the scene in which Vader asks the admiral if he disabled the hyperdrive on the Falcon. This scene is backwards, as you can tell by the insignia on the admiral's chest. Normally it should be on the left side of the chest, but in this scene, it is on the right side of his chest.
Continuity mistake: When the AT-AT that Luke destroyed with a thermal detonator falls over, Luke is nowhere to be seen, even though he should be visible, judging from his position in the previous shot. (As noted in another mistake, the AT-AT is suddenly further away from him after he falls to the ground, but he is still to close to be out of shot when it falls over.). (00:31:45)
Revealing mistake: When Leia and Lando are holding off the stormtroopers while Chewbacca and the droids escape into the Millennium Falcon, a stormtrooper comes running through the doorway. You can see the burn mark on his armour before Lando shoots him. When the trooper is shot, another trooper comes running through the door, also with a burn mark on his armour. Then Leia shoots another (or perhaps the same) trooper, and the burn mark is once again there before the trooper is hit (watch in slow motion). (01:44:20)