Just before Vader ignites his saber for the first time in Cloud City, you can clearly see the actual uncolored rod. However, it isn't white like in the first film but dark gray which blends in against Vader's costume. The best way to see it is to wait until he ignites his saber, then rewind the film with your eye on where the lightsaber was and you'll see it clear as day.
Han the ventriloquist
When Han and Leia are in the cockpit of the Milleium Falcon while they were in the belly of the space slug, Leia says, "Captain being held by you is hardly enough to get me excited". At the same time, if you look closely at Han's lips you'll see that he's saying it with her in unison. Reportedly, Fisher later confessed to being on drugs at the time of the filming and had temporarily forgotten her lines.
Switching horses (or lightsabers) in the middle of the stream
Just after Luke knocks Vader off the deck in Cloud City, he walks around a large machine and doesn't shut his saber off, you can see him reach back and trade for a hilt with a hidden stagehand.
Potato shoe
Just as the Millenium Falcon is entering the asteroid field, you can see out the window of the Falcon two asteroids, one is a potato, the other is a shoe!
Darth has pity on Luke
When Luke and Vader are fighting on Cloud City, as Vader is using the force to hurle boxes and objects at Luke, Luke falls over the edge and the next scene shows him hanging from a catwalk with BOTH hands. Notice: If both hands are occupied, shouldn't he have lost his lightsaber? However, in the next scene he's got it again! Vader must have given him a spare one :)
The force, or the trampoline?
When Luke is fighting Vader on Cloud City, after he knocks Vader off the edge, he jumps down behind him. If you look and listen closely, you hear him hit a trampoline-like device. Then, his head magically reappears at the bottom of the screen for a brief moment.
Someone gave Luke a hand
When Luke is tumbling in the air shaft after the fight on Cloud City, there is a very short scene (just before he gets dropped out the bottom of Cloud City) where you can see his right hand, which had already been sliced off by Vader, still intact.
How does Lando do that?
As Lando is escorting Leia, Han, and Chewie to dinner on Bespin, Lando and Han switch sides from one shot to the next. In one shot, Han is on Leia's right with Lando and her left and in the next shot, as they head down the last bit of corridor to the dining room, Han is on Leia's left with Lando on her right. Han stays on the left for the rest of the scene and pulls out his blaster to shoot Vader in that position.
Double Protection
On Hoth, when Leia gives the 'Okay' to closing the shield doors, watch carefully as Chewie puts his head down as Leia nods. You can see the doors closing, without sound, behind Chewie's shoulder. Then you can see them closing with the appropriate sound afterweards.
Elbow Trouble
Just after Han and Leia have their little "discussion" on board the Millenium Falcon inside the space slug, when you see C-3PO about to tap Han on the shoulder, you can see a mechanism fall from the droids elbow. It is intact in the next scene.
