Revealing mistake: Right before Luke nicks Vader in the shoulder with his lightsabre, Vader cuts through a railing. There's a hole in the railing exactly where Vader apparently cuts it. Also, if you play it in slow motion, Vader's lightsabre never comes into contact with the railing, yet it sparks.
Revealing mistake: When the Falcon leaves Hoth and is being chased by the Empire, there is a scene where the ship gets rocked about. During the 'impact', C-3PO's arm becomes dislodged, and you can clearly see human skin underneath.
Continuity mistake: When one of the Storm Troopers unties 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.
Audio problem: After Luke frees himself from the cave in the beginning, he stumbles towards the exit. You can hear his lightsabre go off, but it stays firmly on. Cut to him emerging, and now his lightsaber's off.
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: After Boba Fett's ship, Slave 1, takes off, there's a close-up of Leia's face. In the background, Lando can be seen standing erect, putting his hands on his waist. In the next shot, he's crouching, with his hands in front of him.
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).
Revealing mistake: When Leia and the crew return to cloud city to rescue Luke from the scaffolding, watch very closely as Lando ascends up the lift, just after the top hatch opens from the overhead angle, you will see that Lando has been replaced with a G.I. Joe look-alike figurine.
Continuity mistake: When the Millennium Falcon jumps into hyperspace at the end of the film, Leia, Luke and Lando are in the cockpit, being tossed back. In the next shot of the cockpit, Lando is missing.
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.).
Continuity mistake: After Luke crashes during the battle on Hoth , the AT-AT is far away from him and is moving rather slowly. A few shots later, the AT-AT stomps on his snowspeeder, but it was too far away from him in the previous shots to reach it that quickly.
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.
Other mistake: When Luke and Leia are watching the Millennium Falcon leave at the end of the movie, its light goes through Luke's arm.
Continuity mistake: When Lando is talking to Han and Leia in the cell in Cloud City, Leia says, "And we're the bait." As the shot ends, her hand is on the nape of Han's neck, but in the next shot, her hand is on his back.