Continuity mistake: After Luke first sees Boba Fett in Cloud City, he begins to walk away from the corner he is hiding behind. In the next shot, he is closer to the corner than in the previous shot. This has nothing to do with camera angles - notice the distance between him and the wall to his left. Also, his right arm is in a different position. (01:34:55)
Continuity mistake: In one shot while Luke is being trained on Dagobah, look at R2 when Yoda says, "Anger, fear, aggression, the dark side of the force are they." The little projection nozzle that sticks out of R2's head is on the left side of the red light (it's on the right side for the rest of the movie).
Continuity mistake: After Leia, Han and Chewbacca walk down the stairs in the carbon-freezing chamber, as the shot ends, Han is turning towards a stormtrooper behind him. In the next shot, he is turned in a different direction, and Leia's head is facing another way. The position and existence of some of the people around them changes between the two shots as well. (01:31:10)
Continuity mistake: During Luke's and Vader's lightsaber duel, Vader says, "Release your anger" and in the next shot their interlocked lightsabers have switched positions.
Continuity mistake: After the carbonite block is pulled out of the carbonite freezer, there's a close-up of Leia leaning towards Chewbacca. In the next shot, she is not leaning on him, and then Chewie pulls her towards him again. (01:33:05)
Continuity mistake: When Luke is holding on to the antennae-like assembly underneath Cloud City, right before and after the hatch closes, the distance between a thin pole and his left arm keeps changing between shots. (01:48:25)
Continuity mistake: When Vader cuts through the three poles at the end of the lightsaber duel, Luke is crouching down next to them. In the next shot, he is standing upright. (01:45:50)
Continuity mistake: When Luke is first attacked by the wampa (ice creature), the amount of blood on him changes between shots.
Continuity mistake: When Vader cuts through three poles at the end of the lightsaber duel, there are different poles in the shot where he cuts through them and the next shot where they fall. (01:45:50)
Continuity mistake: When a one-legged 3PO is standing in the Millennium Falcon, begging R2-D2 to fix him, he is holding the severed leg by the knee, with the foot closest to the floor. Some shots later, he is holding it by the foot, with the knee closest to the ground.
Continuity mistake: When Lando releases Leia and Chewbacca, as Leia says, "What do you think you're doing?" her body is turned in a different direction from the previous shot, and she's holding the blasters differently. (01:37:55)
Continuity mistake: When Janson (Wedge's gunner) fires the harpoon at a leg of an AT-AT, in the first shot of the snowspeeder flying around the AT-AT, the speeder casts a shadow on the snow. In all other shots of this sequence, there is no shadow of the snowspeeder.
Continuity mistake: When Han is trying to keep Luke warm, his rank insignia badge alternates between being on the right and left side of his chest. The amount of snow on Han and Luke's clothes also changes repeatedly, especially Luke's.
Continuity mistake: When Han and Leia kiss in the Millennium Falcon, Leia's arms are around Han's head in the wideshot, but not in the close-up. (00:49:55)
Continuity mistake: Viewed from inside, the hotel where Leia, Han and Chewbacca are in Cloud City has a flat glass roof, but viewed from outside, it is flat with sloped edges. (01:22:25)
Continuity mistake: During the escape from Hoth, C-3PO is far behind Han and Leia as they are running to the Millennium Falcon after the cave-in blocks their path. When they reach the door, he is much closer to them. (00:32:40)
Continuity mistake: During the escape from Cloud City, Chewbacca is shooting at the stoormtroopers while R2-D2 tries to open the door. The wall he is hiding behind keeps changing between shots, and the burn mark on the wall also changes a few times, without any laser beams hitting it.
Continuity mistake: When the Millennium Falcon jumps into hyperspace at the end of the film, Leia, Luke and Lando are in the cockpit, being tossed back. In the next shot of the cockpit, Lando is missing. (01:54:20)
Continuity mistake: When Vader is seen in Cloud City, Lando says, "I had no choice, they arrived right before you did" and two of the stormtroopers on the lowest step are standing about a metre apart. In the following close-up of Lando, they are standing so close together that their ankles are touching. This can only be seen in the widescreen version. (01:25:05)
Continuity mistake: When the Millennium Falcon is approaching Cloud City, Leia's hand is on the top of Han's pilot seat. In some shots, her hand is in the middle of the seat, in other shots, it is right next to the middle.
Answer: The vision Luke sees in the cave on Dagobah is a clue to this. Luke is realizing he has a lot more in common with Darth Vader than the idealized father he'd always imagined. When Vader tells him he's his father, Luke doesn't want to believe it, but he simply can't deny that it feels much more true that his father would be someone passionate and reckless like himself rather than someone who exemplifies a noble Jedi, which feels like an obvious myth in hindsight.
TonyPH