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: 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.
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.
Revealing mistake: At the start of the Vader vs. Ben lightsaber battle, when Ben turns his on, a cord can be seen that runs up Ben's sleeve.
Continuity mistake: When the Jawas arrive to sell the droids, Luke walks over to R5-D4 (the "R2 unit with a bad motivator"), and the droid is standing in front of R2-D2 on Artoo's left. In the next shot, the two droids are standing perfectly next to each other, and there are several Jawas around them that weren't there in the previous shot.
Continuity mistake: In the Detention Block, Han and Luke are in their stormtrooper outfits and are firing at the enemy. They go to a shot of Han then to Luke. Luke's white shoulder pads of his stormtrooper outfit are clearly missing, and you can see a black undergarment. They then go back to Han and then back to Luke again, where the shoulder pads are now back. (01:15:20)
Continuity mistake: During the binary sunset, the two suns are closer together in the close-up than in the wide shot. There is also a cloud and a mountain in front of the lower of the suns, which weren't there in the wide shot.
Continuity mistake: When Vader picks up the rebel in a choke grip, the legs of the stormtrooper in the doorway behind them are apart. In the shot of the rebel's feet, the trooper's legs are together. When Vader tosses the dead rebel into the wall, the trooper's legs are apart again.