Continuity mistake: In the trash compactor, after the dianoga roars, there's a close-up of Leia standing straight up, with her arm over the large iron pole. In the next shot, she is crouching, and her arm is underneath the pole. (01:16:40)
Continuity mistake: When Luke and Obi-Wan enter Docking Bay 94 in Mos Eisley, as the first shot ends, C-3PO is turned to his left and is standing right behind Obi-Wan on Obi-Wan's left. In the next shot, Threepio is turned to his right, and is standing further away from Obi-Wan, behind him on Obi-Wan's right. (00:52:25)
Continuity mistake: Widescreen version: In the trash compactor, as Han says: "What an incredible smell you've discovered." Leia is leaning against some garbage, and then turns her head. In the next shot, she is no longer leaning against the garbage, and her head is turned another way. (01:16:05)
Continuity mistake: In the scene where Alderaan is destroyed, the "buns" on each side of Leia's head are positioned higher up than in the previous scene she was, so that her earlobes are visible. When Luke and Han rescue her, her hair is back to normal. She's held prisoner in a cell, so it's not likely that she could or would have changed her hairstyle.
Continuity mistake: In the scene where Vader chokes the imperial officer with the force, watch him before he gets choked. On his left (your right) of his blue and red button things, he has a pocket with what looks like two pens sticking out. But in a later shot, only one "pen" is sticking out. Later, it goes back to two again.
Continuity mistake: When Luke starts to lead C-3PO and R5-D4 to the garage, some of the droids in front of the sandcrawler repeatedly change position. For example, as Luke says, "And the red one, come on." R2-D2 is standing next to the boarding gantry, but in the previous and following shot, he was standing by the front treads.
Continuity mistake: When everyone is getting in fighters for the final battle, they all have white helmets with blue insignias. However, they aren't wearing them when they're flying.
Continuity mistake: After the droids land in the desert C3-PO has a streak of oil running down his left shoulder. A couple of scenes later when he is walking after he splits up from R2-D2 there is a long shot of him and he still has the streak on his left shoulder. There is an immediate close up and the streak switches to the right shoulder.
Continuity mistake: In the original version of the film, when Luke and C-3PO are searching for R2-D2 outside the moisture farm, in the shot where Luke says, "It's too dangerous with all the Sand People around. We'll have to wait until morning", the sky changes colour. This has been fixed in the Special Edition.