Continuity mistake: After the Millennium Falcon has left Hoth and Han is trying to repair the hyperdrive, in the shot after he asks for alluvial dampers, the tool box Chewbacca gives him can be seen in the lower left hand corner. When Chewie takes the box, it is lying in a different position than in the previous shot. As Chewie walks over to Han, he is holding the right side of the box with his right hand, but as he puts it down, he is holding the left side of the box with his left hand. There are also more tools in the box than in the previous shot.
Other mistake: When the Millennium Falcon escapes Hoth and is pursued by the Star Destroyers, frantic movements cause them to collide. Watch the interior shot of the Star Destroyer as everybody is thrown around. Near the bottom of the screen one of the computer consoles comes away from the wall and is hurridly pushed back into place by a controller!
Continuity mistake: When Leia briefs a group of Rebel pilots in the hangar on Hoth, the position of her head changes completely between the first and the second shot. As the second shot ends, she begins to turn around, but in the next shot, she has already turned around. Also, Major Derlin's (the man dressed in grey) head has changed position.
Revealing mistake: Right after Luke and Darth fight for the first time, Darth gets kicked off of the Carbonite freezer. Then Luke jumps down to fight him again. After he jumps, you hear what sounds suspiciously like a trampoline. Then in the lower right screen you can see Mark Hamill's head pop back up into frame. Widescreen only, although the sound is audible on the 4:3 version too.