Revealing mistake: In the first shot of Luke riding on Hoth, the tauntaun leaves no tracks in the snow. (00:02:50)
Revealing mistake: When Luke is talking to Han over the comlink, there's a shot of Han riding a tauntaun. The animal leaves no tracks in the snow. (00:03:35)
Visible crew/equipment: When the Wampa (ice creature) kills Luke's Tauntaun, the end of the "glove" used as the Wampa's arm can be seen in the bottom left corner, as well as the arm of the crew member wearing it. Widescreen only. Note that this has been fixed on the 2011 Blu-ray release. (00:03:55)
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: The Wampa changes when we see it again in the ice cave. Its fur is less fluffy and its horns are bigger. (00:04:00 - 00:08:45)
Continuity mistake: When Han first walks into the command center on Hoth, there's a shot of Leia looking at him. The shot has been flipped. This can be seen, for example, from that the men on either side of her have switched sides. (00:04:50)
Continuity mistake: When Han and Leia are bickering in the corridor on Hoth, Han says, " Well, the bounty hunter we ran into on Ord Mantell changed my mind." In the next shot, behind them, there's a man walking past them that wasn't there in the previous shot. (00:05:55)
Continuity mistake: When Luke is hanging upside down from the roof of the ice creature's cave, his legs are apart. But in the close-up of his feet, his legs are together. (00:08:40)
Audio problem: In the Special edition, after Luke frees himself from the cave in the beginning, he stumbles towards the exit. You can hear his lightsaber go off, but it stays firmly on. Cut to him emerging, and now his lightsaber's off. (00:09:30)
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 Luke is attacked by the ice creature all the scars are on the right side of his face, but right before he talks to Obi-Wan you see a big scar on the left side of his face, then when he talks to Obi-Wan you can see there are no scars on the left side of his face. (00:11:00 - 00:13:05)
Revealing mistake: After Luke escapes from the snow monster, he collapses, and there's a shot of Han riding. When the camera pans down, there are no tracks in the snow where the tauntaun just ran. (00:11:00)
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)
Audio problem: At the beginning, when they close the door of the hangar, it makes no sound on the first shot. (00:11:45)
Continuity mistake: On Hoth, the hangar's door starts closing twice. (00:11:45)
Continuity mistake: At the rebel base, Leia is informed that there is nothing more can do about Han and Luke until the morning and agrees to the hangar doors being closed. In the wide shot, you can see the doors starting to close, although the code hasn't been put in yet. In the next shot the code is put in and the doors start closing again. (00:12:10)
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 Ben appears to the injured Luke (on Hoth), Luke is reaching out with his left hand calling, "Ben. Ben." As Han appears, Luke is found with his right arm reaching out. (00:13:35)
Continuity mistake: When Han is trying to keep Luke warm, his rank insignia badge alternates between being on the right and left side of his chest. The amount of snow on Han and Luke's clothes also changes repeatedly, especially Luke's. (00:14:15)
Visible crew/equipment: When the Snow Speeders are looking for Luke and Han, you can see the blue screen reflected on the angled side of the pilots' goggles. (00:16:00)
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