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: When the dianoga grabs hold of Luke in the trash compactor, his legs are together. In the next shot, they are much further apart. (01:17:05)
Continuity mistake: In the Cantina, the burly alien threatening Luke pulls out his blaster twice, once in the background when Luke crashes into the table, and once as Ben's lightsaber is heard being ignited. (00:45:05)
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: When Luke and his uncle buy C3-P0 and a white-and-red R5-D4 robot from the Jawas, the R5 unit blows up after travelling a few feet. There's a quick shot of R2-D2 back at the Jawa's transport, and behind R2 you can see the same white-and-red R5-D4 unit being worked on by the Jawas. In the next shot it is back over with Luke. (00:19:15)
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: After C-3PO is separated from R2-D2 on Tatooine, when he's walking among the sand dunes, the sky alternates between being clear and cloudy. (00:10:15)
Continuity mistake: In the trash compactor, as Han says, "I've got a bad feeling about this", Leia's arm is held straight, but in the next shot, it is bent. (01:18:15)
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: Just after the scene where R2-D2 is riding shotgun on Luke's X-Wing fighter and is hit by a shot from Darth Vader, there's a shot of C3-PO standing beside Leia in the rebel HQ, and the dent on C3-PO's head is on the right side (it's on the left side throughout the rest of the movie). (01:56:20)
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 cantina, the alien who eventually gets his arm cut off is hassling Luke. In one shot he puts his hand on Luke's shoulder, but in the next his hand's nowhere in sight. (00:44:40)
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 Luke, Han, Leia and Chewbacca are going into the Millennium Falcon to escape from the Death Star, a storm trooper is shot and falls twice into the pit. (01:32:30 - 01:32:36)
Continuity mistake: Right before Luke yells at Han after he fires his blaster in the trash compactor, there's a wideshot where Han is sitting among some garbage and holding his blaster with one hand. In the next shot, he has turned the other way and is standing, holding the blaster with two hands. (01:16:15)
Continuity mistake: When they are searching for the monster in the garbage compactor, the garbage is shaking, except in one shot.
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.