Continuity mistake: When Han and Leia try to use a pole to stop the trash compactor, Leia says, "Help me." Two shots later, Han can be seen lifting the pole. In the next shot, Leia is suddenly lifting it with him, and Han is holding the pole differently. (01:18:40)
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. (00:11:20)
Visible crew/equipment: When Luke and Leia are stuck on the bridge, just before the stormtroopers arrive on the opposite platform Luke remembers the cable and sees the thruster like things over the top of him and Leia, when we get a view of them a small shadow bobs up and down at the centre bottom of the screen.
Continuity mistake: Just after Obi Wan kills the two aliens in the Cantina, there are two quick "reaction shots" from both ends of the bar. If you are quick, you can see that they are both shots of the same end of the bar with one shot flipped. You can see the same human with the light blue/dark blue suit on in both shots.
Continuity mistake: After Darth Vader kills Obi-Van Kenobi, Luke shouts "No!" and then there is a gunfight with stormtroopers. During this, R2-D2 is seen going up the ramp into the Millennium Falcon. But a few shots later, when Han Solo says "Come on!", you can see R2-D2 at the bottom of the ramp and he going back into the Falcon for a second time.
Continuity mistake: In the trash compactor, Han says, "One thing's for sure, we're all going to be a lot thinner." In the next shot, Han and Leia are both standing in a totally different position. For example, both of them are looking in another direction, and Han's left hand is in a different position. (01:20:15)
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: For this one, you will need a letterbox copy that is not the special edition. In the final award scene, there is a long shot of Luke, Han, and Chewie walking through rows and rows of Rebel Troopers. If you look quickly, the troopers on both ends of the screen are cardboard cutouts. They are cropped off in the Pan and Scan version, and digitised in the special edition, so it has to be the right copy to see this mistake.