Continuity mistake: Several times during the Death Star battle when the Rebel ships are flying down the trench, their position in relation to the chasing TIE Fighters change. For example, sometimes the Imperials are just behind and then nowhere in sight when, next shot, they are back in close firing range.
Continuity mistake: On the journey from the Cantina to the Millennium Falcon the camera pans left to right to follow the actors as they walk first towards and then away from the camera, towards the hangar. At the beginning of the shot R2-D2 is heading in one direction, the droid leaves the frame momentarily and at the end of the pan, trundles into the shot from an impossible angle.
Continuity mistake: Moff Tarkin has fourteen little blocks of color that perhaps indicate rank, seven in two rows. The ones on the top are consistently blue, but at least once the ones on the bottom alternate from orange and red to just orange.
Continuity mistake: When the heros reach Yavin (the Rebel Base) there is a shot of them getting off a cart. Han's holster is on the wrong leg, and Artoo's small lens is on the wrong side. The film was obviously flipped to keep the visual flow of the scenes.
Continuity mistake: Near the end of the Vader/Obi-Wan duel, Luke and Co. run up to the Millennium Falcon. Luke says something along the lines of "Ben?" and it cuts to a shot from roughly behind Luke that shows Vader and Obi-Wan. Look closely: Obi-Wan already has his lightsaber straight up and Vader is going in for the kill. It then cuts to a shot of Obi-Wan glancing over at Luke. Obi-Wan then proceeds to raise his lightsaber (again) for the famous Jedi-disappearing trick as Vader slashes at him (again).
Continuity mistake: Sometimes during the scene in the trash compactor, Leia's sleeves move up and down her arms between consecutive shots. This is best seen in the widescreen version.
Continuity mistake: When Luke and Leia are stopped in front of the pit, one stormtrooper arrives at the other side and shoots at them. Two others arrive later but in the following shot, there's only two stormtroopers, not three. One has disappeared and there's one dead on the floor that we have never seen dying. After that, the dead one disappears and two stormtroopers arrive again - it's the same shot as the beginning, only from another angle. Then, there's one that gets shot and falls in the pit and the dead stormtrooper reappears on the ground.