Other mistake: Widescreen version only: When the stormtroopers are searching for hiding Rebels in the blockade runner, Leia pokes her head out from her hiding place. In the next shot, in the lower left hand corner, something white sticks out behind the foremost "pillar" and then disappears out of view.
Other mistake: In the beginning of the movie, when Leia is uploading a message into R2, we can see C3PO looking for R2. When they show C3PO, there are rebel soldiers behind him, running through the corridor, being shot at and falling down. If you look closely, you can see a black stripe vertically running down in the middle of the doorway.
Other mistake: 2004 DVD edition. As Jabba and Han finish their conversation, Jabba turns to his left as Han moves toward the Millenium Falcon. At the end of the shot Jabba then exits by continuing to turn to his left; his tail would have made this movement not smooth- Jabba should have had to move it or twist over it or something. Probably comes from the scene being shot with a person in that place and Jabba being added later; the person could certainly have moved like that.
Other mistake: Just before Darth Vader enters the Blockade Runner, there are some kind of tiny white-green lasers in the air. They are sometimes in line with the normal red ones. The stormtroopers and the security guards of Leia are both using red lasers, so there is no reason to see green ones.
Add timeDr Wilson
Other mistake: When Han Solo, Luke, Obi Wan, C3PO and R2-D2 are on their way to the Millennium Falcon for the first time there is a scene where they have to walk down a few stairs. If you look carefully you can see that R2-D2 is struggling to get down the stairs but in the next shot he's down with the others.