Continuity mistake: Just before Luke chops off Darth Vader's hand in the battle at the end of the movie, you can see that the bar has already been cut(the line is visible) to give the illusion that Luke cut through the steel bar with his lightsabre as well as Vader's hand.
Continuity mistake: Just after R2-D2 cuts the net that holds him, Luke, Han, Chewbacca, & C-3PO, you can see that before the Ewoks pop up out of nowhere to see their captured victims, one Ewok just stands there in plain sight waiting for the others to reveal themselves.
Continuity mistake: After the Death Star explodes, Wicket the Ewok comes over to Han and Leia, and Leia puts her hand on his arm, and Han puts his hand on his shoulder. In the next close-up of Wicket, their hands are no longer there. This is best seen in the widescreen version.
Revealing mistake: After the Rebels break into the bunker, a Rebel in the background punches an officer. But if you watch closely or play it in slow motion, the Rebel's hand never comes into contact with the officer's face.
Other mistake: In the original version, when the Rebel fleet reaches the Death Star, Lando says, "Fighters coming in" and the Millennium Falcon flies towards the screen. If you play it in slow motion when the Falcon leaves the screen, you can see two white figures shaped like TIE fighters on the Falcon's underside. As the Falcon leaves the shot, they disappear. This has been fixed in the Special Edition.
Continuity mistake: In the Emperor's throne room, the existence and arrangement of several of the canisters on each side of the lift/elevator changes between shots, several times.
Continuity mistake: When Luke is to be executed, he walks to the edge of the plank, and his feet are side by side as he stops walking. But in the beginning of the next shot, one of his feet is behind the other and we see him take another step.
Continuity mistake: When the droids are hiding behind a tree before R2-D2 shoots off to help Han and Leia, the background changes twice.
Continuity mistake: When Luke and Vader enter the Emperor's throne room, they walk towards the stairs, and as the shot ends, Luke put his foot on the first step. In the next shot, they have suddenly moved further up the stairs.
Continuity mistake: When Leia frees Han from the carbonite, the light shining on the walls and floor keeps changing. For example, watch the light on the right side of the carbonite block.
Continuity mistake: When the droids enter Jabba's throne room, in the shot facing the droids, they are not standing on the same part of the floor as in the previous shot. Also, R2-D2 is facing Jabba, but in the previous shot, he was facing C-3PO.
Revealing mistake: Right before Luke leaps from the speeder bike to the scout trooper's speeder, there's a shot showing the front of the speeders. Notice the area surrounding the speeders in this shot. During the rest of the speeder bike chase, the speeders pass through this area several times, even though they are not flying in circles. This can be seen, for example, from the sunlight hitting the ground and the tree on the left side with a bush in front of it. Also, one of the shots where this area is seen is the shot before the speeders pass two more scout troopers, but the background has been flipped.
Continuity mistake: When Vader's shuttle exits the Star Destroyer in the beginning of the film, it is followed by two TIE fighters. The TIE fighters are far apart, but in the next shot, they're close together.
Continuity mistake: After Luke kills the Rancour, Jabba says, "Bring me Solo and the Wookiee.", and Lando is nowhere to be seen. In the next shot, he is suddenly standing in front of Jabba's platform, and some of the other people have changed position.
Continuity mistake: After Han is released from the carbonite, he falls to the ground, soiling his shirt. In the following shots, the amount of dirt changes continuously between shots. Later, when Han and Luke are brought before Jabba, his shirt is clean.
Audio problem: In the beginning of the space battle, a Mon Calamari says, "Admiral, we have enemy ships in Sector 47.", but his lips don't move.
Revealing mistake: If you watch closely (or play it in slow motion) when the scout trooper punches Han, you can see that the troopers hand never actually comes into contact with is face.
Continuity mistake: On Jabba's sail barge, Luke gets shot in his mechanical hand. This leaves a large burn mark on the back of the hand, but when he swings to the skiff on the rope with Leia, the burn is gone.