Other mistake: After they have escaped from the Death Star, Darth Vader says to an officer that they jumped into hyperspace but when you see Han and Leia speaking in the cockpit of the Millennium Falcon, you can't see that blue colour of the sky distinctive to hyperspace.
Other mistake: When Han Solo, Luke, Obi Wan, C3PO and R2-D2 are on their way to the Millennium Falcon for the first time there is a scene where they have to walk down a few stairs. If you look carefully you can see that R2-D2 is struggling to get down the stairs but in the next shot he's down with the others.
Other mistake: When the Falcon is caught in the tractor beam and is being pulled into the Death Star in the next shot after the Death Squad Commander says, "Air bay 327, we are opening the magnetic field," the stars can be seen through the laser guns if you look very closely. This can only be seen in the widescreen version.
Other mistake: In the original release, the lightsabers are not reflected in Darth Vader's helmet or eyes where the other lights in the shot are.
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.