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: In the trash compactor, after the dianoga roars, there's a close-up of Leia standing straight up, with her arm over the large iron pole. In the next shot, she is crouching, and her arm is underneath the pole. (01:16:40)
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 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: When Han and Leia try to use a pole to stop the trash compactor, Leia says, "Help me." Two shots later, Han can be seen lifting the pole. In the next shot, Leia is suddenly lifting it with him, and Han is holding the pole differently. (01:18:40)
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: After the droids leave the control room of the Death Star, there's a close-up of Luke in the trash compactor, pushing against some garbage. In the next shot, he is pushing against the wall. (01:19:45)
Continuity mistake: In the trash compactor, Han says, "One thing's for sure, we're all going to be a lot thinner." In the next shot, Han and Leia are both standing in a totally different position. For example, both of them are looking in another direction, and Han's left hand is in a different position. (01:20:15)
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: After Luke gets pulled underwater in the trash compactor, he is shown with a piece of garbage on his forehead in one shot. In the next shot his forehead is clean, but in the following shot, the piece of garbage is back again. (01:21:35)
Continuity mistake: There's only grayish objects in the garbage compactor but while Luke and Han are removing their uniform, many orange objects appears in it. (01:22:10)
Continuity mistake: When a stormtrooper stands guard by the door of the control room, the door is low enough for someone to hit their head on. But when C-3PO wants to take R2-D2 "down to maintenance", there is plenty of clearance between the trooper's head and the bottom of the door. This has nothing to do with camera angles, as Threepio is the same height as the trooper, and walks out of the room with no problem. (01:22:40)
Continuity mistake: When Han, Luke and Leia run into the group of stormtroopers, Leia's hair is messy. When Luke and Leia reach the chasm, her hair is back to normal. (01:24:00)
Continuity mistake: When Darth Vader and Ben are fighting, Darth's chestplate is on backwards and the belt "buckle" is as well. It appears that the entire shot was reversed. (01:26:20 - 01:27:15)
Continuity mistake: During the battle between Obi-Wan and Darth Vader, there's a scorched slash mark on the wall to Obi-Wan's right before either saber makes contact with it. A few seconds later Darth slashes his saber in exactly that spot (we can see the scorch mark again before he hits it). (01:26:50)
Continuity mistake: When Leia comforts Luke after Obi-Wan's death, the blanket on his back folds different between shots. (01:30:48)
Continuity mistake: Twice during the lightsaber duel, Ben and Vader inexplicably change sabers as the color jumps from one sword to another. Vader is swinging the blue sword while Ben holds the red one. (01:30:55)
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: After Darth Vader has killed Obi-Wan and walks towards the group of storm troopers onto the Millennium Falcon, Luke shoots the dock door control, successfully closing it, fully blocking Vader's path. In the shot immediately following the door is closing once again. (01:32:45)
Continuity mistake: When Luke is talking to Biggs and Red Leader, R2D2's position jumps as he is being lifted up to the top of the X-Wing. (Widescreen version, Special Edition.) (01:39:15)
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.