Continuity mistake: When Luke is hanging upside down in the monster's cave he uses the Force to get his lightsaber. In the shot from Luke's POV it's about 3/4 buried in snow, but in the reverse it's only about 1/4 buried.
Continuity mistake: When Vader cuts off Luke's hand, as the shot ends, Luke is standing upright, but in the beginning of the next shot, he has already began to drop down. (01:45:55)
Continuity mistake: When Luke is sucked out the window, there are no wounds in his face, nor when he hoists himself up on the platform. But when he runs into Vader again, there are. (01:42:35 - 01:45:10)
Revealing mistake: When Luke runs into Vader again after being sucked out the window, as they are fighting in the control room, watch closely: Vader's lightsabre hits the wall a couple of times, but the explosions are not where the sabre touches the wall. (01:45:20)
Continuity mistake: When Luke first meets Vader in Cloud City, in the shot from behind him after he walks up the stairs, his arms are positioned differently from the previous shot. (01:36:55)
Continuity mistake: When Luke climbs into his snowspeeder, his hair is shorter than when he said goodbye to Han and Chewbacca while on his way to the speeder. When he takes off his pilot helmet on Dagobah, his hair is back to normal.
Visible crew/equipment: In the Hoth sequence, after the asteroid hits near Luke, you can clearly see the boom mike in Luke's goggles on his forehead.
Continuity mistake: Leia and Han become annoyed with C3PO's chattering, and Leia turns him off. However, if you watch him in the background, you can see his body move as he breathes.
Revealing mistake: Before Lando warns the people of Cloud City that the Empire has taken control of the city, Leia shoots a stormtrooper. The burn mark can be seen on the troopers armour before the laser beam hits him. (01:42:40)
Continuity mistake: When Luke uses the Force to lift a rock, there are different rocks in the wideshot and the close-up, and the distance between the rocks on the ground changes between the two shots. (01:05:45)
Continuity mistake: In the shot from behind Luke right before he falls into the carbon-freezing chamber, Vader's lightsabre is pointed at his chest, but in the previous shot, the sabre was held in a different angle.
Continuity mistake: In the second shot of Luke in his X-wing after he leaves Hoth, some white wires on his right are in a different position from the previous shot. This also happens in the third shot of him as he's approaching Dagobah.
Audio problem: When Han punches Lando, his hand never makes any contact with Lando's face, and the sound effect is heard after his hand goes past it. (01:29:20)
Continuity mistake: When Vader attempts to turn Luke to the dark side, he says, "With our combined strength, we can end this destructive conflict and bring order to the galaxy." As the second shot begins, Luke is standing much closer to the structure he's holding onto, than in the previous shot. (01:46:20)