Continuity mistake: After Darth Vader kills Obi-Wan Kenobi, Luke shouts "No!" and then there is a gunfight with stormtroopers. During this, R2-D2 is going up the ramp into the Millennium Falcon. But a few shots later, when Han Solo says "Come on!", you can see R2-D2 at the bottom of the ramp and he's going back into the Falcon for a second time.
Revealing mistake: When the stormtroopers stun Leia, if you watch carefully, you can see that she begins to fall before the beam touches her.
Revealing mistake: When Luke and Leia are trying to pass the pit in the Death Star, Leia shoots at a stormtrooper. The shot passes through him without hurting him.
Continuity mistake: In the trash compactor, Han says, "One thing's for sure, we're all going to be a lot thinner." In the next shot, Han and Leia are both standing in a totally different position. For example, both of them are looking in another direction, and Han's left hand is in a different position. (01:20:15)
Continuity mistake: In the scene where Luke finds the remains of his aunt and uncle, in the shots from behind Luke, the wind is blowing from his left. In the shots facing him, the wind is blowing from his right.
Continuity mistake: During the conference in the Death Star, the back of Tarkin's chair is higher in the wideshots than in the close-ups.
Continuity mistake: Luke is on the Millennium Falcon practicing with the floating orb. When he is done, he goes to shut off his lightsaber and as it turns off he jumps to the right due to a dodgy edit.
Continuity mistake: When Han, Luke and Leia run into the group of stormtroopers, Leia's hair is messy. When Luke and Leia reach the chasm, her hair is back to normal. (01:24:00)
Continuity mistake: When Leia is recording her holo-message to Obi-Wan Kenobi, she pushes a button on R2D2 to finish the message but each time we see the actual message during the film, she turns a huge round button.
Revealing mistake: Special Edition Only: In one of the new Mos Eisley scenes, the speeder goes down a road with two Stormtroopers on each side. The troopers are just mirror images of the ones on the other side of the street. Their movements are exactly the same.
Continuity mistake: When Owen is talking to C3PO, the droid has a wire coming from his head to his back. It's not there in the rest of the film.
Continuity mistake: When Tarkin meets Leia in the Death Star, he touches her chin at a certain moment. His arm is bent, but it's impossible because he is too far from her in the previous and the next shot.
Continuity mistake: If you watch Leia while they're in the garbage compactor, her belt, at various points, has fallen down around her thigh. It moves from her thigh to her waist (depending on the camera angle) during the whole scene.
Audio problem: In the French version of the film, Han Solo tells Obi-Wan and Luke to go to hangar 49. 94 is written at the entrance.
Continuity mistake: In the beginning of the first scene of the duel between Vader and Obi-Wan, their lightsabres are held in different angels between several shots.
Continuity mistake: The first time that Luke plays Leia's message from R2-D2, he jumps back (which looks fine), but C3PO flinches and slips off the little 4" or 5" ledge between him and R2.
Continuity mistake: In the Death Star, when they are running into the Millennium Falcon, Leia tells Luke to come. She is behind a piston of the door but the shot later, she is in front of it.
Other mistake: During the chasm crossfire scene, Leia says, "Here they come" and points the blaster upwards as she aims at the stormtroopers above. But the laser moves downwards.
Other mistake: In two close-ups of Han before he jumps down the garbage chute, you can see make-up smeared on his stormtrooper suit, under his chin.
Continuity mistake: After the dianoga pulls Luke into the water (both the first and second time), Han's blaster changes hands a few times.
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.