Continuity mistake: After Luke is attacked by the sand people, a shot shows that his head is laying to the side. In the next shot, its facing straight up.
Continuity mistake: Wide-screen version only: In the trash compactor, after the dianoga has pulled Luke into the water for the second time, Leia is leaning against some garbage. In the next shot, she is leaning forward, the other way.
Continuity mistake: When Obi Wan introduces the lightsaber, he says, "This is the weapon of the Jedi knight." C3PO is disconnected with his head down and in a lighted archway, with some blankets or something by his left side. A frame later, in a close-up, C3PO's head is up, the archway is 'in shadows and the blankets gone.
Continuity mistake: When Ben first gives it to him, Luke's lightsaber is blue, as it was when Anakin dropped it in Episode III. However, when Luke is training against the sphere en route to Alderaan, the lightsaber definitely has a green, not blue, tint to it.
Continuity mistake: When Ben says to Han in the Millennium Falcon, "In my experience there's no such thing as luck", you can see Han is resting his arm on the surface near the control panel, but in the next scene his arm is no longer on the surface.
Continuity mistake: When the movie starts, during the shooting C3PO and R2D2 come out from a corridor on the left. R2 is looking to the right. A shot later he is looking to the left.
Continuity mistake: When Alderaan is first seen through the Death Star's viewscreen/window, only half of the planet is lit up. The next time we see it, about 75% of it is lit up. (00:54:45 - 00:55:50)
Continuity mistake: When Leia, Chewie, Luke and Han dive into the garbage chute aboard the Death Star, Han is the last to dive in, about 4 seconds after Luke. Once he hits bottom, it takes Han 14 seconds to get to his feet, orient himself, and fire his blaster. Luke tries to warn Han, but Han fires anyway, and the blaster bolt ricochets around the garbage chute. Luke shouts, "It's magnetically sealed! I already tried that!" But Luke never had time to stand up and fire his blaster before Han arrived. Han was only 4 seconds behind Luke.
Continuity mistake: When Luke and Ben enter the cockpit of the Millennium Falcon during the meteor shower, Ben enters the cockpit twice between shots.
Continuity mistake: When Luke and C-3PO run out of the house to find R2-D2, Luke takes out his binoculars and looks through them. The shot cuts back to Luke and C-3PO, where C-3PO has his arms are by his side, but in the next shot, C-3PO suddenly has his right arm raised almost half way. (00:26:45)
Continuity mistake: When Leia comforts Luke after Obi-Wan's death, the blanket on his back folds different between shots. (01:30:48)
Continuity mistake: Darth Vader fires at Luke's X-wing and blows R2D2's top off. Half a second later it shows no damage at all. It's not even scorched. When Luke lands, R2D2's head is destroyed and it's scorched all over. (01:56:15)
Continuity mistake: While Luke climbs the ladder to get into the X-wing's cockpit he asks R2 if the little droid is okay, then as Luke steps up he's holding his gloves in his right hand, but it cuts to the next shot as Luke leaps into the cockpit and the gloves are now suddenly grasped in his left hand. (01:43:50)
Continuity mistake: When Red 10 is destroyed by a TIE fighter during the trench run, inside the cockpit as the craft starts to burn up and explode the pilot and the helmet are completely different to that of Red 10 when seen earlier.
Continuity mistake: When Luke is repairing C-3PO at Ben Kenobi's dwelling, he initially has his hands on C-3PO's arm. In the next shot, Luke now has his hand on C-3PO's shoulder.
Continuity mistake: When Luke and Han are talking about Princess Leia being executed, C3PO is facing the computer console when Luke says "but they're gonna kill her." In the wider shot C3PO is now facing Han with no time to turn around.
Continuity mistake: The guard that gets shot and falls down the stairs disappears when Han and Chewing back up there to escape the advancing stormtroopers coming out of the lift.
Continuity mistake: When the Imperial officer opens the door in the Death Star and sees Chewbacca and Han dressed in an Imperial stormtrooper in front of him, he is seen lifting his head, and in the next shot when we see a close-up of the officer, he is seen lifting his head a second time. (01:08:40)
Continuity mistake: At the dinner table, Luke picks up the container in his left hand to pour. A moment later, he picks it up in his right hand. Also, as Owen explains about Obi-Wan, you see Luke's left hand lifting then lowering the glass. When the shot cuts to Luke's face, his right hand is making the motions.
Continuity mistake: The oil streak on Threepio's left, then right, shoulder has totally disappeared when he's seen in the Sand Crawler.
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.