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.
Continuity mistake: When the Walrusman attacks Luke in the cantina, if you look carefully you can see that the alien has curved hooves instead of hands (behind the scenes photos confirm this.) When Ben Kenobi cuts off his arm, an arm with hairy paws is lying on the floor. We know it is walrusman's arm because the other guy wasn't wearing an orange jacket.
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.
Other mistake: During the attack on the Death Star, in one shot an X-Wing has two blue engines with two pink, while they are all supposed to be pink.
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 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.
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.
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.