Continuity mistake: When Han is put on the platform during the carbon freeze sequence, Darth Vader and Boba Fett are standing behind him and there is no one else in view, but when we see a close up of Han, an Imperial stormtrooper has suddenly appeared. (01:35:55)
Visible crew/equipment: While in hot-pursuit, Han and Chewie are desperately trying to fix the Millennium Falcon (just after C-3PO informs them of the damaged hyperdrive, making light-speed impossible). In one shot Chewbacca has a bare human thumb, without gloves or makeup, and can be easily spotted in the lower left part of the screen. (00:38:00)
Revealing mistake: When Han tricks the three Star Destroyers into running into each other, it cuts to the bridge crew of one destroyer being knocked around by the impact. You can see one of the officers in the 'trench' section (the lower level of the bridge) bump into one of the consoles and knock it askew, revealing it's actually a lightweight prop. For added humor, the officer that was sitting at said console then subtly tries to push it back into position before the scene cuts.
Revealing mistake: Han and Leia are arguing in the ice tunnels near the beginning. Han tells her she wants him to stay, and they stop and talk about it. Two people pass. Han moves back for the first person to come between them. The second alien-looking guy walks behind Han. His rubber mask gets caught on Han's right shoulder and bounces back into shape immediately.
Continuity mistake: When Luke crashes on the snow he tries to open the cockpit pushing the canopy. A shot later he is pushing the windshield. This changes back and forth several times.
Continuity mistake: After Luke's snowspeeder crashes on the snow, right before he exits, there's no damage on the right window. From the outside shot it's broken all over.
Continuity mistake: After Boba Fett's ship takes off, C-3PO yells, "Oh no. Chewie, they're behind you." Chewbacca shoots at the newly arrived stormtroopers and one of them falls over dead, next to the big white sculpture at the top of the stairs. In the next shot, where R2-D2 spins around before going after the others, the stormtrooper's body is gone. (01:43:55)
Continuity mistake: When the Imperial stormtroopers arrive to prevent Leia, Han and Chewbacca from escaping after being captured by Darth Vader, Lobot (Lando's aide) walks down the steps and stands in front of two of the stormtroopers. When we see Lando saying "I'm sorry" in the next shot, Lobot has disappeared. (01:28:40)
Continuity mistake: When the Falcon is being pursued by the Star Destroyers after escaping Hoth, C-3PO enters the cockpit, attempting to talk with Han, but the ship shakes and he lands on Chewie. After Han says to check the deflector shields, Chewie pushes C-3PO off him, though C-3PO leaves his hand on Chewie's shoulder. In the next shot, C-3PO is suddenly standing at the other end of the cockpit, with his hand nowhere near Chewie. (00:37:10)
Continuity mistake: Before Han is frozen in carbonite, you can see there is nothing by Leia. When the platform Han is standing on begins to drop, we return to Leia and she now has an Imperial stormtrooper standing by her. (01:36:10)
Audio problem: When Lando is punching desperately at the door's control panel in Cloud City, he says "The security code has been changed!" but his mouth doesn't move when he says it. (01:47:10)
Continuity mistake: In the original 1980 release of The Empire Strikes Back, the group accompanied by Billy Dee Williams just walked from the deck with the Falcon inside the halls of the city. There is a man fixing a wall and next to that man is a window, the window shows a blue sky with a couple of buildings that were obviously drawn in the scenery. However in the last scene where Harrison Ford was hugging Billy Dee Williams the sky was orange. This shot only last for a second as the round small window is drawn wrong. But all of cloud city is a painting so its no surprise.
Revealing mistake: When the stormtroopers are firing at Chewie and the droids and C3PO is yelling at R2D2 about the Millennium Falcon's hyper-drive, there is a shot of Chewie being shot at and the beam putting a hole in the wall. In one shot, it doesn't look much bigger than a pinpoint, but in the next shot, the team at Industrial Lights and Magic were kind enough to add a CGI burn mark, which contracts, almost disappears, and then warps as smoke passes in front of it, wrecking the illusion. (01:48:10)
Continuity mistake: When the Millennium Falcon goes towards the bottom of Cloud City towards the end of the movie, we cut to the inside of the cockpit and Lando says "Look, someone's up there" when he notices Luke on the weather vane. At this point you can see Lando's right hand is on Chewbacca's seat when he says this, but when the camera is behind Lando in the next shot, his right hand is no longer on the seat. (01:54:30)
Continuity mistake: When Luke is lying in the snow after escaping from the Wampa, his gun holster is on the left hand side, but when Han finds him, the holster is now on the right hand side. (00:13:00)
Continuity mistake: When Han, Leia and Chewbacca are captured by the Imperials in Cloud City, Lando says, "I'm sorry", to which Han replies, "I'm sorry too." At this point, Chewbacca is looking at Lando, but as the shot changes he is looking at Han, and then looks at Lando a second time.. (01:28:50)
Answer: The short, short answer to this is "Yes... from a certain point of view." The long answer is complicated and depends completely on what timeframe you mean by "always." If you're going back all the way to the early rough drafts of the early-mid 70s (which actually resemble Episode I more than they do the Star Wars of 1977), you'll find there's a cyborg father figure protagonist that makes a heroic sacrifice, and then another character that is a "black knight" villain that eventually turns to the side of good near the end. Just to make things more complicated, there is yet another character, a villain by the name of "Darth Vader" that is a human Imperial officer like Grand Moff Tarkin. It may be a stretch to count all that as "Darth Vader was always the father" but the pieces were all there, at least.
TonyPH
(1) Now the earliest explicit mention on any documented material that Darth Vader is Luke's father comes from notes Lucas made outlining the general story of the trilogy and its place in the larger Star Wars saga. These were found in the archives for The Empire Strikes Back, but they are undated and we don't know if they were written before Star Wars (1977) and carried forward, or if they were written afterward. These were found fairly recently (made public in 2010) and as far as I know Lucas has never commented publicly about them.
TonyPH
(3) One thing we know, at least, is that Lucas had come up with the idea of Darth Vader the father before starting work on The Empire Strikes Back. Something incredibly odd, though, is that the first draft written by Leigh Brackett does not feature the twist (and in fact introduces Anakin himself as a ghost); for a long time many fans took this as proof that Lucas hadn't thought of the idea at all by then, but after the series outline was discovered it was made apparent that Lucas simply hadn't told Brackett for some reason. Perhaps he wasn't sure yet that he wanted to go through with it, or maybe at that point he was thinking of revealing it in the third film. Either way, Lucas would write the second draft himself, and that's where the twist first appears in script form.
TonyPH
(2) Something that must be understood about Star Wars (1977) is that it was an ALTERNATIVE to his original plans of a saga. By then he didn't think it was realistic that he would be able to make a long series of many movies, so he came up with a "Plan B": he crammed the general story of the trilogy into one movie. So we know that when Star Wars (1977) was filming, Darth Vader was NOT Luke's father, because this one movie was IT, that was the whole story. But what we DON'T know, is whether that means Lucas had abandoned the idea of Vader being the father in order to simplify the story, or if Lucas simply hadn't thought of that at all just yet.
TonyPH
(2, cont.) On a side note, you can tell by watching Star Wars (1977) how it has condensed the story of the trilogy. The middle portion has the characters trying to escape capture from the Empire while one of them loses a duel with Darth Vader (like The Empire Strikes Back) and the third act is a final battle against the Death Star above a forest moon (like Return of the Jedi). The first act features a member of royalty on the run while a couple of protagonists find the main hero on a desert planet, resembling the original drafts and by extension Star Wars: Episode I. Because of this we've arguably never actually had a "pure" first chapter to the original trilogy, even though Lucas eventually had the film serve this purpose anyway.
TonyPH