Continuity mistake: When Luke is in Obi-Wan's home, C-3PO tells him "Sir, if you'll not be needing me, I'll close down for a while." and Luke nods. However, when R2-D2 projects Leia's recording, C-3PO turns his head to look at it. (This is only just visible). (00:35:06)
Continuity mistake: During the scenes in the trash compactor, after Han fires his blaster, the burn marks on the door keep changing shape, size and position. In some of the wideshots, they disappear completely.
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)
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.