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: 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 trash compactor, as Han says, "I've got a bad feeling about this", Leia's arm is held straight, but in the next shot, it is bent. (01:18:15)
Continuity mistake: When Luke and his uncle buy C3-P0 and a white-and-red R5-D4 robot from the Jawas, the R5 unit blows up after travelling a few feet. There's a quick shot of R2-D2 back at the Jawa's transport, and behind R2 you can see the same white-and-red R5-D4 unit being worked on by the Jawas. In the next shot it is back over with Luke. (00:19:15)
Continuity mistake: When Luke returns after dinner, he comes back and finds C-3PO hiding. When Luke finds out that R2-D2 is gone, he runs out of the room and outside. But you see the stairs he runs up to get outside. When you see Luke arrive and takes out the micro-binoculars C-3PO is right behind him. There is no way that C-3PO is that quick to keep up with a younger Luke. What did he do run?
Continuity mistake: When the rebel leaders are studying the tactical illustration of the Death Star, the superlaser's dish is positioned on the battle station's equator. The Death Star's dish is actually offset from its equator, in the station's northern hemisphere. This was because the early CGI used to create the tactical readout of the plans took so long to make that by the time it was finished, the Death Star's design had been changed to offset the superlaser dish, and due to 1970s technology, there was no time left before the movie's release to change the plans, which were accurate to an earlier design of the station.
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: Just after the scene where R2-D2 is riding shotgun on Luke's X-Wing fighter and is hit by a shot from Darth Vader, there's a shot of C3-PO standing beside Leia in the rebel HQ, and the dent on C3-PO's head is on the right side (it's on the left side throughout the rest of the movie). (01:56:20)
Continuity mistake: After C-3PO is separated from R2-D2 on Tatooine, when he's walking among the sand dunes, the sky alternates between being clear and cloudy. (00:10:15)
Audio problem: [Special Edition only] In the scene where Luke and Leia swings across the missing bridge, a number of the shots fired by Leia are "bangs" instead of the laser "zap" sound. The bang is probably from the prop gun used (it shot blanks) and was never dubbed over (until the 2004 DVD release).
Continuity mistake: The microphone on Red Leader's helmet switches from one side of his face to the other, then back again as he pulls out of the Death Star trench (just before he crashes). (Actually the entire shot is mirrored. Check out the scuff marks on the centre of his helmet, they change direction as well.) Other shots and pilots' mics switch too: Red Leader when he says, "All wings, report in", Wedge after a shot of Leia and C-3PO monitoring the battle, Luke when Red Leader says, "There's a lot of fire coming from the right side of that deflection tower" and when Luke says, "I'm hit, but not bad".