Continuity mistake: When Darth Vader kills Obi-Wan Kenobi, there is a gunfight between Luke, Han and stormtroopers. While this is happening, Vader is seen leaving the hallway, but in one shot he is back in the hallway standing on Obi-Wan's cloak.
Continuity mistake: Widescreen version: In the trash compactor, before the scene where the droids leave the control room, both ends of the pole used to stop the compactor are coming into contact with the walls. After the droids leave the room, the right end of the pole is not coming into contact with the wall. (01:18:50 - 01:19:45)
Continuity mistake: When Luke sees Red Leader hit the Death Star surface, an explosion appears out of nowhere and the X-Wing is not seen at all. Furthermore, the plummeting ship would have spread debris over a much wider area considering it was falling at such a shallow angle. (01:48:30)
Continuity mistake: When they are leaving Mos Eisley Han wears gloves, but when he pulls the lever to jump into hyperspace, they disappear. (00:54:15)
Visible crew/equipment: When the Blockade Runner is being attacked, just before C-3PO says something like: 'Do you hear that?' to R2-D2, he turns his head and the camera crew is visible on his temple.
Continuity mistake: When R2D2 is captured by the Jawas, a Jawa welds a restraining bolt to the middle of a panel on R2. When the shot changes to a close up, it's being attached to the top of the panel. The shot changes again, and it's welded to the middle again.
Continuity mistake: In the garbage crushing facility, when the walls are coming in, you see them with about 15 feet space, then it zooms to the actors, they talk for about 5 seconds, and then it zooms out again with still 15 feet of space. The walls are coming in for about a minute. At the rate they were moving, they should have been crushed in around 20 seconds.
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.
Continuity mistake: Just after the creature lets Luke go, Leia says, "It could be worse." In the next shot (after the compactor makes its first sound), Luke can clearly be seen saying, "What's that?", but his question has been edited out.
Continuity mistake: When Luke and R2 are doing the trench run, a tie shoots at Luke and blows the top of R2's head off. But in the next scene R2's top is on again.
Revealing mistake: When the Millennium Falcon exits from hyperspace where Alderaan was, a TIE fighter follows them. There is a shot where it passes in front of the Falcon and then disappears.
Continuity mistake: During the Death Star trench run, Wedge quits because his X-Wing is damaged. The sky behind him changes from grey to black in the same shot.
Continuity mistake: Widescreen version: In the trash compactor, Han says to Leia, "Get on top of it." In the next shot, Leia can be seen in the background, in a totally different position from the previous shot. For example, she is holding the pole differently. (01:20:25)
Continuity mistake: When Luke sees the holograph of Princess Leia for the first time, and says, "Who is she, she's beautiful," Mark Hamill's hair is rather tousled. In the next shot of him, it's neatly combed. Then, when he gets up and says, "Well I don't know anyone named Obi-Wan...," his hair is tousled again!
Continuity mistake: When Luke has been knocked unconscious by the Sand People and Obi-Wan appears and scares them off, there's a shot of Luke lying there and one of his sleeves is in disarray, halfway up his arm. But when Obi-Wan checks his pulse, he does it right through a fully-covered-by-the-sleeve wrist. (00:28:25)
Continuity mistake: When in the Death Star, there is a shot of five stormtroopers standing next to the Millennium Falcon. Two of the stormtroopers are right next to the boarding ramp. The camera instantly changes to a higher point of view and the two stormtroopers have moved about four feet farther away from their original spots.
Continuity mistake: In the scene just before Luke goes to eat dinner, C3PO has a towel or rag in his hand in some scenes, and it is missing in others. This continues as he admonishes R2 about replaying the message.
Revealing mistake: Special Edition: When Luke and Obi-Wan are arriving in Mos Eisley to find a pilot, the Ronto in the background throws the Jawa riding him to the floor. When the Jawa falls to the ground a puff of dust is seen and a thud is heard, but look closely - he never actually hits the ground.
Continuity mistake: When Luke first sees the holomessage from Leia, she is bending down to stop the recording while still saying "Help me Obi Wan Kenobi, you're my only hope." When the message is viewed for the second time, she finishes speaking, looks around, and then bends down to stop the recording.
Continuity mistake: After the Stormtroopers have captured Leia aboard the Blockade Runner and are leading her to Vader, one Stormtrooper's armour is visibly damaged (http://s253.photobucket.com/albums/hh67/RoofingGuy/BrokenStormy.jpg). For the close-up of Leia, the damage has been masked with white gaffer tape (http://s253.photobucket.com/albums/hh67/RoofingGuy/FixedStormy.jpg). [Timecode from 2008 Widescreen DVD release. similar time on the "Theatrical Release" bonus disc.]. (00:07:25)
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.