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.
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: 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.
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.
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: In the scenes in the conference room in the Death Star, the black hemisphere on the conference table changes position between shots.
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: The first time Chewie gets into the cockpit of the Millennium Falcon, he hits his head on a small set of dice. They aren't seen in subsequent shots, nor are they seen in the rest of the trilogy.
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.
Continuity mistake: In the scene where stormtroopers are firing at the Millennium Falcon as it leaves Mos Eisley Spaceport, watch the trooper on the far left. After he is shot he begins to fall, then suddenly he's standing again in the next shot, where he begins his fall again. This happens two or three more times, this falling and straightening.
Continuity mistake: In the end scene, when they blow up the Death Star, whether the camera is on the Ties or X-wings, the enemy is never visible in front or behind them.
Continuity mistake: In the wide screen version, after Luke, Han, Chewy, Obi-Wan and the droids come out of the hidden cargo bins in the Falcon, Obi-Wan says "Who's the more foolish, the fool or the fool that follows him." Then he tries to lift himself out of the bin...it looks as if he doesn't quite have the strength to do it - he puts his arms on the side, exerts a bit of pressure, and waits for the cut.
Continuity mistake: In the scene where R2-D2 is rolling down a path on Tatooine, under the eyes of scavenging Jawas, the path he is traveling on can be seen to end several feet in front of R2, and beyond it is a rough, rocky surface that R2-D2's wheels could not possibly traverse. In the next shot, R2 is rolling down a suddenly extended (or perhaps the same?) path towards capture.
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.