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).
Other mistake: When the stormtroopers break into the control room, the stormtrooper on the right of the screen hits his head on the door frame. On the DVD release they've added a thump when he hits it.
Revealing mistake: When Darth Vader and Ben are fighting, Darth's chestplate is on backwards and the belt "buckle" is as well. It appears that the entire shot was reversed.
Revealing mistake: On the Jawas' transporter, when R2D2 looks around in one of the shots, you can very clearly see the actor, Kenny Baker, inside through his eye hole.
Revealing mistake: In the scene at the end of the very first battle, where Imperial troops have just taken control of Princess Leia's rebel ship, Darth Vader breaks the neck of the rebel leader and tosses his body to the wall. The "dead" rebel puts up both of his hands to avoid slamming his face into the wall.
Continuity mistake: When Obi-wan and Luke are watching the hologram of Princess Leia projected onto a small table, the objects on the table change position and number in each shot.
Visible crew/equipment: Just after the Falcon takes off from Mos Eisley, there's a shot of the Falcon with Star Destroyers chasing. The next shot is of Han Solo alone in the cockpit. Watch carefully behind him in the doorway, and you'll see the shoulder of a man in a green shirt quickly move out of shot.
Continuity mistake: After Luke gets pulled underwater in the trash compactor, he is shown with a piece of garbage on his forehead in one shot. In the next shot his forehead is clean, but in the following shot, the piece of garbage is back again.
Visible crew/equipment: In the original widescreen version, during a long shot of a loading bay in the Death Star, you can see a crew member walk just into shot on one side of the screen, stop, look up, and back out again.
Revealing mistake: When the Tusken Raiders are seen raiding Luke's speeder, you can actually see the wheels or at least whatever is holding it up off the ground.
Continuity mistake: In the scene where Luke and Leia are about to swing across the canyon inside the Death Star, Leia shoots one last time. She hits the bulkhead behind the stormtrooper on the right and he falls forward. The trooper on the left continues firing (as seen in the screencap).
Revealing mistake: When an Imperial Officer is running down the tunnel in the Detention Block towards Han, Luke and Chewbacca, Han clearly shoots the top-left hand corner of the tunnel and the Imperial Officer falls down the stairs as if he shot him.
Revealing mistake: In the Death Star corridor leading to the Millennium Falcon, just before Han says "Didn't we just leave this party?" you can see Carrie Fisher and Mark Hammill's shadows on the wall as they await their cue to run in.
Revealing mistake: Just before Lord Vader appears the first time (on the boarded consular ship, through the breached door), there is a Stormtrooper checking another trooper apparently dead on the floor (he's lifting the dead one's head). Then Vader enters, and the Stormtrooper quickly straightens up, dropping the head. It turns out the "dead" Stormtrooper was actually alive, however, because he carefully lowers his own head to the floor.
Visible crew/equipment: When C-3PO is on the Conveyor belt in the Jawas transport vehicle, if you look in the reflection in his head you can see the camera crew.
Revealing mistake: Sand people are up on a hill overlooking a valley below where Luke is passing by in his speeder. One of the sand people takes aim at Luke, but his companion stops him. Right before the end of the shot, as the speeder is traveling towards the lower right corner of the screen, it becomes transparent. This is a multiple exposure shot, and the path of the speeder wasn't quite lined-up right.
Continuity mistake: The first interior shot of the Millennium Falcon's cockpit shows small hanging dice. In every other shot, however, the dice are gone.