Continuity mistake: When everyone is getting in fighters for the final battle, they all have white helmets with blue insignias. However, they aren't wearing them when they're flying.
Continuity mistake: When Darth Vader is interrogating the captain of the Blockade Runner, the stormtrooper on the left behind them has his blaster at his waist but in the shot showing their legs, he has it at his chest. It's at his waist again some shots later.
Continuity mistake: Widescreen version only: After escaping the trash compactor, Leia says, "From now on, you do what I tell you", and Luke's left hand is up by his head. In the next shot, his right hand is up by his head and his left hand is down by his side.
Continuity mistake: After the droids land in the desert C3-PO has a streak of oil running down his left shoulder. A couple of scenes later when he is walking after he splits up from R2-D2 there is a long shot of him and he still has the streak on his left shoulder. There is an immediate close up and the streak switches to the right shoulder.
Continuity mistake: When Han yells at Chewbacca to "Get in there, you big furry ape", Chewie steps in. It cuts away, then cuts back and Chewie steps in a second time.
Continuity mistake: When the Rebel fleet is on its way to the Death Star, there's a shot where the fighters are seen from behind as they approach the Death Star. Given its tremendous size, and the rate at which it is growing larger to our view, their rate of approach must be incredible. But when Red Leader calls, "Accelerate to attack speed", when you consider their speed with their surroundings, they are now going much slower.
Continuity mistake: In the scene where Alderaan is destroyed, the "buns" on each side of Leia's head are positioned higher up than in the previous scene she was, so that her earlobes are visible. When Luke and Han rescue her, her hair is back to normal. She's held prisoner in a cell, so it's not likely that she could or would have changed her hairstyle.
Continuity mistake: When Obi-Wan's spirit instructs Luke to run, Luke is holding his blaster with two hands, and then drops it down by his side, holding it with only one hand. In the next shot, Luke is again holding the blaster with two hands, and repeats the movement.
Continuity mistake: After the escape from the Death Star, when C3PO is stuck in electric wires, there's a shot of R2D2 with the black and red computer panels of the control room in the Death Star behind him.
Continuity mistake: Every storm trooper has 2 pipes with slots besides their masks, but the one that shoots Leia with the stunt gun doesn't have those slots.
Continuity mistake: When Luke returns after dinner, he comes back and finds C-3PO hiding. When Luke finds out that R2-D2 is gone, he runs out of the room and outside. But you see the stairs he runs up to get outside. When you see Luke arrive and takes out the micro-binoculars C-3PO is right behind him. There is no way that C-3PO is that quick to keep up with a younger Luke. What did he do run?
Continuity mistake: When Leia's holo-message is being played in Luke's garage, and C-3PO explains about R2-D2's restraining bolt, the background behind the hologram has been flipped.
Continuity mistake: The microphone on Red Leader's helmet switches from one side of his face to the other, then back again as he pulls out of the Death Star trench (just before he crashes). (Actually the entire shot is mirrored. Check out the scuff marks on the centre of his helmet, they change direction as well.) Other shots and pilots' mics switch too: Red Leader when he says, "All wings, report in", Wedge after a shot of Leia and C-3PO monitoring the battle, Luke when Red Leader says, "There's a lot of fire coming from the right side of that deflection tower" and when Luke says, "I'm hit, but not bad".
Continuity mistake: In the final battle, the leader of the fighters (not the group that was to blow up the Death Star, but the leader of Luke's group), got killed. Then it goes back to the home base where Leia, C3PO, etc are watching the action and you hear a transmission from that leader.
Continuity mistake: When they are searching for the monster in the garbage compactor, the garbage is shaking, except in one shot.
Continuity mistake: During the medal ceremony, there is a close-up of Han followed by a shot of Leia with a big smile. She turns to the right to get a medal, then there is a wider shot of her and she's not smiling.
Continuity mistake: When the walls of the trash compactor start moving, Han is holding the pole, and leans it against the wall to his left (we hear it hit the wall). In the next shot, the pole leaning on the wall to his right instead., and the right side of the pole moves up and down between the next few shots.
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: 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.
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.