Revealing mistake: When the droids head towards Tatooine in their escape pod, a rotating imperial ship is shown in the pod's window, getting smaller as the pod moves away. Regrettably, the star field gets smaller at the same rate as the ship, something that would only happen if you were moving away from a photograph, painting etc. (00:06:55)
Continuity mistake: Special Edition: When Han is talking to Jabba the Hutt, when Jabba begins to says, "What if everyone who smuggled for me dropped their cargo at the first sign of an Imperial starship?", Chewbacca can be seen walking behind them. In the next shot, he is suddenly walking next to a wall that was nowhere near him in the previous shot. In the following shot, he is back to his original position. (00:51:00)
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.