Continuity mistake: After R2-D2 opens the door to the landing platform during the escape from Cloud City, the droid exits through the door. Some shots later, he is back inside. (01:43:55)
Continuity mistake: Leia and Han become annoyed with C3PO's chattering, and Leia turns him off. However, if you watch him in the background, you can see his body move as he breathes.
Continuity mistake: Widescreen version: Darth Vader and Admiral Piett are talking on board the Star Destroyer at the end of the movie. In the first shot, a man is standing behind Piett. In the next shot of Vader and Piett, a different man is standing behind Piett. Then, in the third shot of Vader and Piett, the first man is back. The design of the wall and window also differs. (01:57:05)
Continuity mistake: When Vader is about to tell Luke that he is his father, as Luke says, "He told me enough," he is holding onto one of the thin poles next to him. In the next shot, his hand is positioned lower down and clutching the other pole. Also, his head is in a different position, seen from the markings on one of the other poles. The position of his head and hand changes in the next shot as well. (01:46:35)
Continuity mistake: Widescreen version: When Luke and Vader are fighting in the carbon-freezing chamber, as Vader says, "Only your hatred can destroy me.", the hose hanging from the ceiling behind Luke is pointed straight down, but in the previous shot, it was bent. This has nothing to do with camera angles - watch the smoke coming from it, it changes direction as well. (01:40:40)
Continuity mistake: When Vader addresses the bounty hunters, Piett says, "Bounty hunters-We don't need their scum.", and starts walking towards a corner. In the next shot, he is already at that corner. (01:03:20)
Revealing mistake: Before Lando warns the people of Cloud City that the Empire has taken control of the city, Leia shoots a stormtrooper. The burn mark can be seen on the troopers armour before the laser beam hits him. (01:42:40)
Other mistake: After Vader cuts through a pillar with his lightsaber in the beginning of the duel, the hole in the pillar is much bigger than it should be. (01:37:35)