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.
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.
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.
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.
Continuity mistake: After the Stormtrooper tells Darth Vader the Death Star plans are not in the main computer, when Vader lifts the Rebel off his feet by his throat as the Rebel tells him they intercepted no transmissions, take note of the leg plates on the Stormtrooper to Vader's right. In the wideshot, the Stormtrooper's left leg armor does not have the knee protector plate (it looks as if it's at his right knee because the extra switched them), but in the next closeup the knee plate appears at his left knee, as it should be.
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.
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.