Continuity mistake: When the walls of the trash compactor start moving, the bar Leia uses to brace them is easily obtainable, but in the previous shots, it was partly buried in garbage.
Continuity mistake: During the attack on the Death Star, in one shot an X-Wing has two blue engines with two pink, when they are all pink the rest of the time.
Revealing mistake: When Gold Leader enters the Death Star trench, there's a shot from his cockpit. When Luke, Wedge and Biggs enter the trench later, the same shot is used again. This can be seen from a flash of light accompanied by the sound of a shot, followed by three green laserbolts, then another flash/shot and more laserbolts.
Continuity mistake: When Luke and Obi-Wan are talking to Han in the Cantina, the black cup on the table is sometimes standing right by Han's hands, and sometimes right next to Luke, depending on the camera angle.
Continuity mistake: In the trash compactor, after the dianoga roars, there's a close-up of Leia standing straight up, with her arm over the large iron pole. In the next shot, she is crouching, and her arm is underneath the pole. (01:16:40)
Continuity mistake: In the original version of the film, when Luke and C-3PO are searching for R2-D2 outside the moisture farm, in the shot where Luke says, "It's too dangerous with all the Sand People around. We'll have to wait until morning", the sky changes colour. This has been fixed in the Special Edition.
Continuity mistake: Widescreen version only: When Luke activates his new lightsaber for the first time, the position of C-3PO's head is different from the previous shot. After he turns it off, Threepio's head is back to its original position.
Continuity mistake: In the Death Star, when Luke and Leia are going to jump over the pit, Leia wraps her hands around Luke's neck. In the following shots, her hands are wrapped around his waist.
Continuity mistake: When Luke and Obi-Wan enter Docking Bay 94 in Mos Eisley, as the first shot ends, C-3PO is turned to his left and is standing right behind Obi-Wan on Obi-Wan's left. In the next shot, Threepio is turned to his right, and is standing further away from Obi-Wan, behind him on Obi-Wan's right. (00:52:25)
Continuity mistake: Widescreen version: In the trash compactor, as Han says: "What an incredible smell you've discovered." Leia is leaning against some garbage, and then turns her head. In the next shot, she is no longer leaning against the garbage, and her head is turned another way. (01:16:05)
Revealing mistake: As Princess Leia is about to undergo interrogation by the droid in her cell, the needle bears the legend "Made In England".
Continuity mistake: When Luke first tries his father's lightsaber in Ben's house, it has a blue color but when he is practising on the Millennium falcon, it now has a white or sometimes light blue color. It has nothing to do with lighting because light sabers always have a bright color in the rest of the movie, even in the darkness.
Continuity mistake: Watch Luke's shadow when he walks toward his aunt to talk to her, and when he turns around. In the following shot, where he is walking toward the Jawa sandcrawler, his shadow is cast in another direction.
Revealing mistake: When Luke ignites his new lightsaber in Ben's house, the reflection of the stick used during the filming is visible on C-3PO's body. (00:33:55)
Continuity mistake: In the scene where Vader chokes the imperial officer with the force, watch him before he gets choked. On his left (your right) of his blue and red button things, he has a pocket with what looks like two pens sticking out. But in a later shot, only one "pen" is sticking out. Later, it goes back to two again.
Continuity mistake: When Luke starts to lead C-3PO and R5-D4 to the garage, some of the droids in front of the sandcrawler repeatedly change position. For example, as Luke says, "And the red one, come on." R2-D2 is standing next to the boarding gantry, but in the previous and following shot, he was standing by the front treads.
Revealing mistake: On the Death Star, before Luke and Leia try to cross the pit, Luke shoots a panel to close the door. Firstly, he shoots beside it, and secondly, after it explodes, no electronic components are visible in it.
Continuity mistake: When the rebel leaders are studying the tactical illustration of the Death Star, the superlaser's dish is positioned on the battle station's equator. The Death Star's dish is actually offset from its equator, in the station's northern hemisphere. This was because the early CGI used to create the tactical readout of the plans took so long to make that by the time it was finished, the Death Star's design had been changed to offset the superlaser dish, and due to 1970s technology, there was no time left before the movie's release to change the plans, which were accurate to an earlier design of the station.
Continuity mistake: When everyone is getting in fighters for the final battle, they all have white helmets with blue insignias. However, they aren't wearing them when they're flying.
Continuity mistake: When Darth Vader is interrogating the captain of the Blockade Runner, the stormtrooper on the left behind them has his blaster at his waist but in the shot showing their legs, he has it at his chest. It's at his waist again some shots later.
Answer: It is heavily implied that one who becomes a Force-Ghost achieves an untold level of power upon entering the state. Given that they have become a pure entity of the Force, it seems to back up the statement. Obi-Wan also becomes free to assist Luke in any case.
Darius Angel
In addition to this answer, I think Obi-wan also became powerful because he "let go." He did not feel a need to defeat Vader on this occasion - he was willing to surrender the fight and "move on" to a new state. Something that Vader might not currently understand.