Continuity mistake: Special Edition: When Han is talking to Jabba the Hutt, as Jabba says, "Why did you fry poor Greedo?", the man standing to his left is pointing a blaster towards Han. In the next shot, the man is no longer pointing the blaster at him.
Revealing mistake: After the tractor beam pulls the Millennium Falcon into the Death Star, there's a shot of a MSE-6 droid ("mouse droid") at the feet of four stormtroopers. The trooper in the back right, is holding onto his helmet in a desperate attempt to keep it from falling off.
Continuity mistake: Special Edition: When Han is talking to Jabba the Hutt, when Jabba begins to says, "What if everyone who smuggled for me dropped their cargo at the first sign of an Imperial starship?", Chewbacca can be seen walking behind them. In the next shot, he is suddenly walking next to a wall that was nowhere near him in the previous shot. In the following shot, he is back to his original position.
Other mistake: In the trash compactor, after C-3PO realises that he turned off the comlink, Leia grabs the bar used to stop the compactor and her hand sinks in and puts a dent in the bar. When she loosens her grip, it returns to normal. No wonder it was useless at bracing the walls...
Continuity mistake: As R2-D2 is rolling through the canyon, he's on a smooth part of the land. He then stops and looks around. When he starts moving again, the terrain has changed and is now full of rocks and pebbles.
Continuity mistake: During the conference in the Death Star, the back of Tarkin's chair is higher in the wideshots than in the close-ups.
Revealing mistake: When the droids head towards Tatooine in their escape pod, a rotating imperial ship is shown in the pod's window, getting smaller as the pod moves away. Regrettably, the star field gets smaller at the same rate as the ship, something that would only happen if you were moving away from a photograph, painting etc.
Continuity mistake: When the walls of the trash compactor start moving, the bar Leia uses to brace them is easily obtainable, but in the previous shots, it was partly buried in garbage.
Continuity mistake: In the beginning of the first scene of the duel between Vader and Obi-Wan, their lightsabres are held in different angels between several shots.
Continuity mistake: Widescreen version only: When Luke activates his new lightsabre for the first time, the position of C-3PO's head is different from the previous shot. After he turns it off, Threepio's head is back to its original position.
Continuity mistake: Watch Luke's shadow when he walks toward his aunt to talk to her, and when he turns around. In the following shot, where he is walking toward the Jawa sandcrawler, his shadow is cast in another direction.
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.