Revealing mistake: After Han Solo runs into the room full of stormtroopers, you can see rubber soles under Chewbacca's feet as he follows him. (01:24:15)
Continuity mistake: When R2D2 and C3PO land on Tatooine, the escape pod is on the flank of a dune. When the stormtroopers are doing their investigation, the pod is suddenly on more or less flat sand.
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: The ammo belt of Chewbacca appears on him just before the jump into hyperspace.
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: 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 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.
Continuity mistake: As C-3PO enters the escape pod and says, "I'm going to regret this", he is right in front of the round opening. In the next shot, he has already begun to walk through the opening. (00:06:35)
Continuity mistake: During the binary sunset, the two suns are closer together in the close-up than in the wide shot. There is also a cloud and a mountain in front of the lower of the suns, which weren't there in the wide shot.
Continuity mistake: When the Jawas arrive to sell the droids, Luke walks over to R5-D4 (the "R2 unit with a bad motivator"), and the droid is standing in front of R2-D2 on Artoo's left. In the next shot, the two droids are standing perfectly next to each other, and there are several Jawas around them that weren't there in the previous shot.
Continuity mistake: When Luke is eating with his uncle and aunt, the cup he's drinking from keeps switching hands.
Continuity mistake: In the Detention Block, Han and Luke are in their stormtrooper outfits and are firing at the enemy. They go to a shot of Han then to Luke. Luke's white shoulder pads of his stormtrooper outfit are clearly missing, and you can see a black undergarment. They then go back to Han and then back to Luke again, where the shoulder pads are now back. (01:15:20)
Continuity mistake: When Han and Luke (disguised as stormtroopers), and the "captured" Chewbacca are waiting for a lift in the Death Star, an officer wearing a grey shirt walks by, which changes to an officer wearing a black shirt in the next shot. Widescreen version only.
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.