Continuity mistake: In the lightsaber duel between Luke and Darth Vader, Luke chops off Vader's hand twice before Vader falls down. The first shot shows Luke's lightsaber striking Vader's wrist, and Vader's hand separating from the wrist. The second shot is from behind and shows the lightsaber chopping Vader's hand clean off his wrist, then it sparks.
Continuity mistake: When R2-D2 is tied up in the Ewok village, the rope that binds him keeps changing position.
Continuity mistake: Just before the Emperor's ship lands on the Death Star, a formation of four TIE fighters disappears from the center right of the frame. This happens seconds before the in-hangar scene with Vader greeting the Emperor. This is visible on VHS.
Continuity mistake: After Lando is shot off the transport vehicle when Han is trying to save him, look for Lando to actually walk down the sand in the bottom of the screen. The very next scene, he is hanging on the rope.
Continuity mistake: When Lando orders half the fighters to break off and return to the surface, an A-Wing and an X-Wing break off to the right. When Green Leader acknowledges, the same A-Wing and X-Wing break off to the right again.
Revealing mistake: When Luke jumps from Jabba's prisoner's skiff over to another skiff, if you watch Lando hanging underneath the prisoner's skiff, you can easily see that he is a matte painting in this shot, because he doesn't move at all (visible on widescreen).
Other mistake: When R2-D2 cuts the net, only Han, Luke, and Chewbacca fall from it. Maybe C3P0 would have held for a moment because his leg was stuck in the net, but R2 was right over the hole.
Continuity mistake: When Luke takes off Vader's mask, we see Anakin Skywalker with eyebrows on him, but in Revenge of the Sith, Anakin burns on Mustafar and his hair and eyebrows are gone. This has been fixed on the 2004 release.
Revealing mistake: In an overhead shot of Darth Vader throwing the Emperor to his death down the Death Star reactor, you can see that it is a dummy in the Emperor's costume and not Ian McDiarmid.

Continuity mistake: When Luke is riding the speeder bike against the trooper, the black glove on his right hand jumps to his left and then back again. (01:01:15)

Other mistake: During the fight between Luke and Darth Vader, when Vader throws his lightsaber at Luke, it is not only Luke's lightsaber from Episodes IV & V instead of his own, it is ignited upside-down, with the blade protruding from the pommel rather than the emitter. (01:50:20)
Audio problem: After R2-D2 gets shot, Leia says to Han, "I'll cover you.", but the words don't match the movement of her lips. (01:39:00)
Audio problem: When the shuttle Tydirium is approaching Endor, look closely when Han says, "Fly casual" - he begins to say the words before his lips start moving. When he stops talking, his mouth is still moving.
Continuity mistake: When Anakin Skywalker (Vader) dies, the path of a tear is visible under one of Luke's eyes. Two shots later, the tear path is dry. (01:55:45)

Revealing mistake: Vader tosses the Emperor and then collapses on some barrels next to the railing. Look at Vader's arm - the one with the severed hand. His arm is bent at the forearm in a way that arms just don't bend. This is because David Prowse's hand was inside an "elongated" arm to simulate it being chopped off. He couldn't keep his wrist straight, giving the appearance of a bent forearm. (01:57:00)

Revealing mistake: When Jabba's sail barge begins to explode, you can see that one of the floating skiffs is standing on stilts. (00:36:30)
Continuity mistake: In the scenes where the Emperor is trying to convert Luke, watch the stars through the window behind him. The same group of stars go floating past every time.
Continuity mistake: Look at the full body shot of the holographic Luke. Luke, who normally has his lightsaber clipped to his left hip, now has it hung from his right hip. As well, his hair, which normally has a part on his left hand side, is now parted on the right. Afterwards, just before Artoo turns the message off, we get a shot from behind Artoo, and Luke's hologram is visible on the extreme right of the screen. Luke's lightsaber is now hanging from his left hip where it normally is.
Audio problem: In the desert after Luke starts putting his rescue plan into action, Han says "Boba Fett", before hitting him unintentionally. He immediately says "Boba Fett" again. It is the same sound, looped.
Other mistake: On Endor, after Han Solo's group was captured, C-3PO called out to the Empire's soldiers. One of them said "Bring those two down here!" Both C-3PO and R2-D2 were up there, but from the Imperials were standing, they could only see C-3PO. R2 was hidden behind a tree. They wouldn't know that he was there until they actually got close to the two.
Answer: The Jedi are shown to have something of a blind spot in regards to matters of the heart. Note that when Luke confronts Obi-Wan over lying to him about his father's fate, Obi-Wan's response is haughty and defensive, and gives Luke nothing in terms of regret or apology. They're focused on their mission, not on how Luke feels. Why waste time, in their eyes, telling Luke about his mother? If they had their way, he wouldn't even know about his father. The prequels would make this more explicit, showing that the Jedi are conditioned from the beginning to let go of all "passions" because they could so easily be corrupted, and their inability to understand Anakin's emotions just contributes to his downfall.
TonyPH