Revealing mistake: If you watch carefully before Han Solo shoots Greedo, you can see that Greedo has been replaced with a faker looking goofy dummy just before he explodes. (00:48:45)
Continuity mistake: Viewed from outside, the Millennium Falcon has 4 windows around a round one, but view from inside, there are only three. (00:52:25 - 00:53:55)
Revealing mistake: As Luke prepares the line and grappler to swing across the shaft, Leia provides cover fire. In one close-up, you can see a cartridge case being ejected from the 'blaster gun'.
Continuity mistake: In the Cantina, look at the walrus-like alien in a orange space-suit near Luke. He has hairy paws, but when he pushes Luke, he has normal hands with leather gloves and hairy paws again when Obi-Wan cuts his arm.
Continuity mistake: Moff Tarkin has fourteen little blocks of color that perhaps indicate rank, seven in two rows. The ones on the top are consistently blue, but at least once the ones on the bottom alternate from orange and red to just orange.
Continuity mistake: The ammo belt of Chewbacca appears on him just before the jump into hyperspace.
Revealing mistake: Special Edition. When Han is speaking to Jabba in the hangar, when they are talking about the percentage, or something like that, Han says that 20% is too much. When he says that, his sleeve passes through Jabba's arm.
Continuity mistake: Near the end of the Vader/Obi-Wan duel, Luke and Co. run up to the Millennium Falcon. Luke says something along the lines of "Ben?" and it cuts to a shot from roughly behind Luke that shows Vader and Obi-Wan. Look closely: Obi-Wan already has his lightsaber straight up and Vader is going in for the kill. It then cuts to a shot of Obi-Wan glancing over at Luke. Obi-Wan then proceeds to raise his lightsaber (again) for the famous Jedi-disappearing trick as Vader slashes at him (again).
Continuity mistake: When Luke and Obi-Wan are stopped by the Storm Troopers and Obi-Wan uses his mind trick on one Trooper, there are a couple of other Troopers standing at Obi-Wan's side at first, but when they are cleared to pass, they disappear.
Continuity mistake: When the heros reach Yavin (the Rebel Base) there is a shot of them getting off a cart. Han's holster is on the wrong leg, and Artoo's small lens is on the wrong side. The film was obviously flipped to keep the visual flow of the scenes.
Continuity mistake: When Luke uses the comlink to call up C-3PO to ask how to get out of the detention block, a rack with 3 blasters can be seen in the control room. But right before the stormtroopers enter the control room, there are suddenly 4. (01:14:45 - 01:18:55)
Continuity mistake: The windows in the cockpit of Darth Vader's ship are arranged differently when viewed from the inside or outside.
Continuity mistake: When Luke is talking to Biggs and Red Leader, R2D2's position jumps as he is being lifted up to the top of the X-Wing. (Widescreen version, Special Edition.) (01:39:15)
Other mistake: In the Cantina, look at the little alien at the bar, the one which makes mice sounds. Each times he drinks, he doesn't touch his mouth, but his chin with his glass.
Continuity mistake: Sometimes during the scene in the trash compactor, Leia's sleeves move up and down her arms between consecutive shots. This is best seen in the widescreen version.
Revealing mistake: At the start of the Vader vs. Ben lightsaber battle, when Ben turns his on, a cord can be seen that runs up Ben's sleeve.
Continuity mistake: When Chewbacca and C-3PO are playing holographic chess, there's the black and red set of the control room in the Death Star behind the droid whenever there's a closeup on him.
Audio problem: When C-3PO lowers himself into the oil tub, as Luke says, "It just isn't fair." his head is shown from the side and he then turns his head away from the camera, but the words don't match the motion of his jaw (or his lips, if you look closely). (00:19:00)
Other mistake: Just after Obi Wan strikes down the two aliens in the Cantina, there are quick "reaction shots" from both ends of the bar. If you are quick, you can see that one of the shots is flipped. You can see the same aliens and human with the light blue/dark blue suit on, that were in an earlier shot of that side of the bar.
Continuity mistake: When Luke and Leia are stopped in front of the pit, one stormtrooper arrives at the other side and shoots at them. Two others arrive later but in the following shot, there's only two stormtroopers, not three. One has disappeared and there's one dead on the floor that we have never seen dying. After that, the dead one disappears and two stormtroopers arrive again - it's the same shot as the beginning, only from another angle. Then, there's one that gets shot and falls in the pit and the dead stormtrooper reappears on the ground.
Answer: While planning Star Wars, Lucas had a vague notion of doing a long series of movies inspired by old serials, then dropped that idea in favor of just one. When Star Wars became a phenomenon and sequels became feasible, Lucas revisited the idea. He thought of three trilogies along with some stand-alone "in-between" stories for a total of 12 films. By the time of The Empire Strikes Back's release, this was pared down to the 9 mainline films, going by interviews with Lucas and the cast at the time. By Return of the Jedi, Lucas had decided to end the saga there, with the option that he could revisit the first three at some later point. It's unclear if Lucas ever had any specific story ideas for the proposed sequel trilogy, and they never had any scripts. Producer Gary Kurtz suggested in an interview they would've been about Luke's twin sister (not Leia), though many fans are skeptical about just how much he would know about them. Of course since this question was asked a sequel trilogy was written and released.
TonyPH