Continuity mistake: When the Imperial officer opens the door in the Death Star and sees Chewbacca and Han dressed in an Imperial stormtrooper in front of him, he is seen lifting his head, and in the next shot when we see a close-up of the officer, he is seen lifting his head a second time.
Deliberate mistake: During the 4 Tie Fighter attack you can see the blue screen octagon matte leftovers surrounding the Tie's trying to blend into space. However it's not the same type of black, so they glow a bit. They are constantly confused as shields, but they aren't. It's real easy to spot if the contrast and lighting on your TV is a bit high, but I spotted it without that.
Continuity mistake: When Obi Wan introduces the lightsaber, he says, "This is the weapon of the Jedi knight." C3PO is disconnected with his head down and in a lighted archway, with some blankets or something by his left side. A frame later, in a close-up, C3PO's head is up, the archway is 'in shadows and the blankets gone.
Continuity mistake: When the dianoga grabs hold of Luke in the trash compactor, his legs are together. In the next shot, they are much further apart.
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.
Revealing mistake: During Darth Vader and Ben's lightsabre duel, sometimes you can see a white wire attached to Ben's lightsabre, for example after he says, "If you strike me down, I shall become more powerful than you can possibly imagine."
Audio problem: When Luke, Han, Chewie, Ben and the droids are in the control room, and Luke says "but they're going to execute her," watch closely: his mouth doesn't move for half the sentence.
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).
Continuity mistake: During the shoot out on Tatooine the same stormtrooper can be seen falling in the background from 3 different angles as Han boards the Millennium Falcon.
Continuity mistake: When Luke and Ben enter the cockpit of the Millennium Falcon during the meteor shower, Ben enters the cockpit twice between shots.
Continuity mistake: When Ben says to Han in the Millennium Falcon, "In my experience there's no such thing as luck", you can see Han is resting his arm on the surface near the control panel, but in the next scene his arm is no longer on the surface.
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.
Continuity mistake: When the rebel leaders are studying the tactical illustration of the Death Star, it shows a large, round indentation positioned at the Death Stars equator. The Death Star actually has a smaller, round indentation in its northern hemisphere. Can't be due to intentional differences between the plans and the finished thing, otherwise the rebels would have no way of knowing that the vulnerability was still there either.
Continuity mistake: When Han yells at Chewbacca to "Get in there, you big furry ape", Chewie steps in. It cuts away, then cuts back and Chewie steps in a second time.
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.