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: 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). (01:01:25)
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. (01:44:50)
Continuity mistake: In the wideshot where Luke lets himself fall down the pit in Cloud City, Vader lowers his outstretched hand. In the following close-up, he lowers it again. (01:52:10)
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. The poles that are cut have a white color, while the ones that fall are dark grey. (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. (01:59:00)
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: 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: In the shot where Luke's hand is cut off, there's a large gash in his shirt on his left shoulder. In the following shots, the gash is much smaller. (01:50:20)
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 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. (01:47:55)
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. (01:18:35)
Continuity mistake: When a blast rocks the command centre during the battle on Hoth, C-3PO is thrown backwards into Han's arms. As the wideshot leaves, Threepio is leaning backwards, supported by Han, but in the next shot, both of them standing upright in a normal way. Toryn Farr, the woman sitting behind them, has changed position as well. (00:30:40)
Continuity mistake: When Chewbacca is choking Lando, as Leia says, "We don't need any of your help.", Lando is standing on his knees. In the next shot, only his head can be seen, but the position of his head and Chewie's arms shows that he is now standing straight up. In the next shot, he is on his knees again. (01:38:15)
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: 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 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 Luke is first attacked by the wampa (ice creature), the amount of blood on him changes between shots. (00:04:00)
Continuity mistake: When Luke summons his lightsaber back to his hand during the duel, he's holding onto a hose with his other hand. He is holding it differently from the previous shot. (01:40:25)
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