Continuity mistake: As noted in another mistake, when Han, Leia and Chewbacca are taken captive in Cloud City, two of the stormtroopers change position between shots. This also happens to some of the other troopers, as well as to Lobot, Lando's aide. This is best seen in the widescreen version.
Continuity mistake: Special Edition: Luke cuts off the Wampa's arm at the shoulder, but the limb seen hitting the cavern floor is way too short to be the entire arm. (00:09:30)
Continuity mistake: When the Rebels pick up the signal of the Imperial probe droid, general Rieekan says, "Princess - we have a visitor." In this close-up, his head is straight, but in the next shot, he is standing in a different place, leaning forward. (00:17:35)
Continuity mistake: When Han gets off the taun-taun when he is searching for Luke, the upper part of his jacket and the garment over his chin is covered in snow. In the next shot facing Han, the snow is gone.
Continuity mistake: As Major Derlin and another Rebel officer talk before the shield doors are closed, another officer walks under the starship Leia's standing by. In the next shot, he's gone. (00:11:30)
Continuity mistake: When Vader attempts to turn Luke to the dark side, the wires hanging from the structure that Luke is holding onto change in number and position between several shots.
Continuity mistake: When Luke uses the Force to lift a rock, the rock is much higher above the ground in the close-up than in the wide-shot. (01:05:45)
Continuity mistake: When Luke is standing on his hands while using the Force to lift a rock, he is distracted. As he collapses, the rocks on the ground are different and in a different position from the rocks seen in the shot before Yoda says, "concentrate." (01:06:00)
Continuity mistake: When Luke drops down in pain after his hand is cut off, he is not holding onto the pole with his other hand (watch closely), but in the next shot, his hand is now clutching the pole. (01:46:00)
Continuity mistake: At the rebel base on Hoth, the Falcon is being repaired in a hollowed-out snow cave. When Han blasts off out of the cave, none of the debris on the floor or in the cave moves at all, nor is there any effect from the Falcon's exhaust.
Continuity mistake: In the beginning of the scene where Luke meets Yoda, in the shots facing Yoda, his hands and walking stick are positioned in front of his face or shoulder. In the shots from behind him, they are positioned in front of his chest.
Continuity mistake: When the Millennium Falcon is pursued by the Star Destroyers after escaping the space slug and, Han pulls the lever for the hyperdrive. In the next shot from behind, the lever has not been pulled.
Continuity mistake: After the Millennium Falcon has left Hoth and Han is trying to repair the hyperdrive, in the shot after he asks for alluvial dampers, the tool box Chewbacca gives him can be seen in the lower left hand corner. When Chewie takes the box, it is lying in a different position than in the previous shot. As Chewie walks over to Han, he is holding the right side of the box with his right hand, but as he puts it down, he is holding the left side of the box with his left hand. There are also more tools in the box than in the previous shot.
Continuity mistake: When Leia briefs a group of Rebel pilots in the hangar on Hoth, the position of her head changes completely between the first and the second shot. As the second shot ends, she begins to turn around, but in the next shot, she has already turned around. Also, Major Derlin's (the man dressed in grey) head has changed position. (00:23:05)
Continuity mistake: When Luke has the vision of Obi-Wan, the amount of snow lying on his back and arm changes significantly between shots. In some shots, he is covered in snow, in others, most of it is gone.
Continuity mistake: On Hoth, when the rebel troops starts to see the At-ST, there is a shot where rebels take place for the battle and there is destroyed equipment and black smoke in the air, even though the battle has not started.
Continuity mistake: When the Empire ship shoots asteroids in the asteroid field, the first one explodes before the laser even hits it.
Continuity mistake: In the last part of the lightsaber duel, and in the following scenes, the color and seriousness of the wounds and bruises on Luke's face keep changing: For example, in the iconic segment where Luke reacts in shock and horror at Vader revealing himself to be his father, the injuries look quite nasty, but when he comes to a stop inside the tunnel after falling from the catwalk, they look far less severe. (01:49:30)
Continuity mistake: When Boba Fett shoots at Luke, he fires his blaster four times. The second shot hits the corner Luke is standing by, but in the next shot of Luke, there is no burn mark there. The only burn mark seen is the one from the third shot. (01:35:05)
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)
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