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: 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).
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 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.
Add timeSuper Grover
Continuity mistake: When a stormtrooper stands guard by the door of the control room, the door is low enough for someone to hit their head on. But when C-3PO wants to take R2-D2 "down to maintenance", there is plenty of clearance between the trooper's head and the bottom of the door. This has nothing to do with camera angles, as Threepio is the same height as the trooper, and walks out of the room with no problem.
Continuity mistake: During the battle between Obi-Wan and Darth Vader, there's a scorched slash mark on the wall to Obi-Wan's right before either saber makes contact with it. A few seconds later Darth slashes his saber in exactly that spot (we can see the scorch mark again before he hits it).