Deliberate mistake: After the Tusken Raider has attacked Luke, he raises his stick over his head and shouts. The movement of his clothing is extremely unnatural. During the editing, they put the same footage forward, then backward many times, to add emphasis to his movements, but it looks decidedly odd.
Deliberate mistake: When Obi Wan deactivates the Death Star's force field, there's an electronic gauge going down and a sign in clear English with the word POWER - as we've seen in shuttles and other places, they don't use English. The studio decided it was better to show "power" and "tractor beam" in English so that the audience would know what Obi-Wan was doing. The lettering we see in Jedi doesn't really affect the plot, so it doesn't need to be English. Still doesn't really fit though. This is fixed on the DVD.
Deliberate 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.
Deliberate mistake: As noted in another mistake, Red Leader's helmet microphone changes sides before he crashes. Because some shots during the attack on the Death Star are flipped, this also happens to Rebel pilots earlier in the battle: Red Leader when he says, "All wings, report in", Wedge after a shot of Leia and C-3PO monitoring the battle, Luke when Red Leader says, "There's a lot of fire coming from the right side of that deflection tower" and when Luke says, "I'm hit, but not bad" and finally Red Leader after Gold Leader is killed.
Deliberate mistake: During the 4 Tie Fighter attack you can see the blue screen octagon matte leftovers surrounding the Tie's trying to blend into space. However it's not the same type of black, so they glow a bit. They are constantly confused as shields, but they aren't. It's real easy to spot if the contrast and lighting on your TV is a bit high, but I spotted it without that.