Trivia: Anakin Skywalker's first name is first mentioned in this film. His name comes from a friend of George Lucas, British film director Ken Annakin.
Suggested correction: Actually his first name first revealed in Empire Strikes Back when he is on call with the Emperor. He says, "I have no doubt that this boy is the offspring of Anakin Skywalker."
Anakin's name was not used in the original release of "The Empire Strikes Back", therefore the trivia is correct. George Lucas retconned the special edition release and added "Anakin." Originally Luke was referred to as the "son of Skywalker."
Revealing mistake: After the Rebels break into the bunker, a Rebel in the background punches an officer. But if you watch closely or play it in slow motion, the Rebel's hand never comes into contact with the officer's face. (01:33:25)
Revealing mistake: During the lightsaber duel, Vader throws his at Luke. The catwalk behind Luke explodes, but if you watch in slow-motion there are two explosions: one some inches over where the lightsaber actually hits and one far on the left.
Suggested correction: If you have to use slow motion to see something, it's not a mistake.
Revealing mistake: In the scene where Han and Chewie sneak up on the two storm troopers on the Endor moon, Han steps on a twig, it snaps, and the trooper turns around and punches him. Watch in slow motion as the punch is released, Han starts falling backwards before the fist hits him.
Suggested correction: If you have to use slow motion to see something, it's not a mistake.
Stupidity: Leia was carrying a handheld bomb. Yet she doesn't think to bring it with her later on while freeing Han.
Suggested correction: Novels from the Expanded Universe make it clear that with the exception of guards, nobody is allowed to carry weaponry in Jabba's Palace.
Factual error: The cockpit for the Falcon is on the right side of the ship. Why, from the inside, does it always look like it's directly in the center of the front of the ship? The visuals outside are not offset like they should be for a cockpit that's not in the middle of the ship.
Suggested correction: They're not offset - you can't see the rest of the ship to the left because of where the cockpit windows are. We're just looking forwards into space.