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 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.
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.