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 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: A few seconds before the Detention Block shootout begins, the 2 Death Star Troopers pull out DH-17s but after the fight begins and it cuts back to the Trooper on the left, he is holding an E-11.
Continuity mistake: After Obi-Wan is struck down there's a shootout where a soldier is killed next to a closing door. The gun next to his head moves closer between shots.
Visible crew/equipment: When Leia and the others come back to the rebel base, she says "there's no time for sorrows." The camera is moving during this shot and its shadow is cast on the actors.
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: 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.
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 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: During the shoot out on Tatooine the same stormtrooper can be seen falling in the background from 3 different angles as Han boards the Millennium Falcon.
Continuity mistake: When Ben and Luke enter the cockpit of the Millennium Falcon after leaving Tatooine, Ben is seen standing behind Chewbacca on his seat, but in the very next shot he is seen standing by the seat.
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.