Continuity mistake: When Yoda and R2-D2 are engaged in a tug-of-war over the little flashlight, Yoda hits him several times with his walking stick. When Artoo lets go, the stick is pointing upwards as Yoda hits him one last time, but in the next shot, Yoda is using it as a walking stick again and it is pointing downwards.
Continuity mistake: When the Millenium Falcon escapes from the giant space worm, it comes from the center of the mouth, but viewed from outside, it comes from the side.
Visible crew/equipment: A boom microphone is reflected in Luke's goggles when he says "Hey, what's the matter? You smell something?"
Revealing mistake: Look carefully at the end of the cavern where the Millenium Falcon enters the giant asteroid. It's a dark blue circle, because the light is dim. But there is a little white circle on the right and the two circles are much brighter on the left side. It's because it's an image of a planet with a moon.
Visible crew/equipment: When the snowspeeders exit the rebel base to go to the battle, there are rails under them.
Revealing mistake: If you closely when Vader cuts through the three poles at the end of the lightsaber duel, you can see that the saber never actually goes through the poles. (01:45:50)
Continuity mistake: When Luke is hiding behind a corner in Cloud City right before he signals to R2-D2 to keep silent, his blaster is held in different angles between the shot from the back and the shots facing him. (01:35:00)
Revealing mistake: When we see the Star Destroyer for the first time, there are three of them on screen. The one on the top left, can still be seen even after another Star Destroyer came into frame and blocks the view.
Revealing mistake: If you look closely when Vader cuts off Luke's hand, you can see that Vader's lightsaber never actually cuts through Luke's wrist, but passes in front of his hand. (01:45:55)
Continuity mistake: Widescreen version: After Vader chokes Captain Needa, he talks to Admiral Piett. The distance between Piett and the officer next to him differs between shots, depending on the camera angle. (01:10:55)
Continuity mistake: After R2-D2 opens the door to the landing platform during the escape from Cloud City, the droid exits through the door. Some shots later, he is back inside. (01:43:55)
Continuity mistake: There is a shot from inside the cockpit, just before Luke's snow speeder crashes. Look at the speeder's legs, the proportions are wrong. According to this shot the snow speeder must be tiny.
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: On Hoth, the hangar's door starts closing twice. (00:11:45)
Continuity mistake: When Luke is carrying Yoda on his back, as he says, "But tell me why I can't," his head is turned to his left, but in the previous and following shot, he is facing forward. (00:39:55)
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: When the Empire ship shoots asteroids in the asteroid field, the first one explodes before the laser even hits it.
Continuity mistake: When Darth Vader and Admiral Piett are talking on board the Star Destroyer at the end of the movie, in the first shot, a man is standing behind Piett. In the next shot of Vader and Piett, a different man is standing behind Piett. Then, in the third shot of Vader and Piett, the first man is back. Widescreen version only.
Continuity mistake: When Vader is about to tell Luke that he is his father, as Luke says, "He told me enough," he is holding onto one of the thin poles next to him. In the next shot, his hand is positioned lower down and clutching the other pole. Also, his head is in a different position, seen from the markings on one of the other poles. The position of his head and hand changes in the next shot as well. (01:46:35)
Continuity mistake: When Luke and Vader are fighting in the carbon-freezing-chamber, Vader says, " You have learned much, young one." Their light sabres are held in different angles between this shot and the previous and following shot. (01:39:40)
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