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)
Other mistake: During the scene when Obi-Wan is sneaking around the Imperial ship, a group of stormtroopers march by in a close group. One of the troopers is losing his armour and is attempting to hold it on.
Revealing mistake: Sand people are up on a hill overlooking a valley below where Luke is passing by in his speeder. One of the sand people takes aim at Luke, but his companion stops him. Right before the end of the shot, as the speeder is traveling towards the lower right corner of the screen, it becomes transparent. This is a multiple exposure shot, and the path of the speeder wasn't quite lined-up right. (00:27:55)
Visible crew/equipment: When the Falcon is in the Death Star hangar, a scanning crew is sent aboard to find passengers, one of the stormtroopers walks straight past the camera and its shadow is visible on his leg. (01:01:55)
Continuity mistake: When Leia shoots a hole in the detention area wall for their escape, the hole is not big enough to jump through, but when they all jump in, the hole is much bigger. (01:15:10)
Revealing mistake: When Luke and C3PO are outside of the farm searching for R2D2, a droid passes in front of them. You can see lines in the sand, either to keep the robot in a straight line, or where the wheels of the robot have gone in earlier takes. (00:26:50)
Audio problem: When Vader is talking to an Imperial officer in the hangar in the Death Star, when the officer says, "It must be a decoy, sir. Several of the escape pods have been jettisoned." his head is shown from behind, but his profile shows his mouth is moving before the words are heard. (01:03:55)
Revealing mistake: In the scene where the "torture" robot goes to get information from the princess, if you look carefully on the side of the syringe you will read "monoject", which is an American hypodermic syringe manufacturer. (00:41:30)
Revealing mistake: When Darth Vader flies out of the Death Star you see the light falling on the back of the ship change as he clears the bay. Later, when he regains control of his spinning fighter the same shot with the falling shadow is used to show him flying away. (01:49:30)
Revealing mistake: You can see the arm of the crane used to lower the torture device through the door when it is going into Leia's room. (00:41:15)
Revealing mistake: When Luke first ignites his lightsaber, he turns it from the right side of the screen to the left side. When the blade is facing the screen, the lightsaber appears flatter than in the previous shot. (00:33:50)
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: In the scene after Carrie Fisher inputs the Death Star plans into R2-D2 the droid moves towards C3-PO along a corridor. As you watch you can follow R2's movements until the camera cuts away. If the shot were to continue it seems clear that R2 would have banged into a piece of set protruding from the side of the corridor. (00:05:15)
Continuity mistake: Sometimes, the red stripes on the wings on the underside and topside of Luke's X-wing change. For example, compare the shot where he brushes his hand along the underside of the wing of the ship prior to the battle, and the shot before he says, "I'm hit, but not bad."
Continuity mistake: Special Edition DVD. When Luke, Obi-Wan and droids arrive at space bar in Mos Eisley, notice the herder with white jacket followed by a dinosaur-creature on a leash and then the R2 unit. In the next shot the dinosaur and R2 are there, but the herder has disappeared. (00:42:20)
Continuity mistake: In Mos Eisley, when Ben and Luke are interrogated by the stormtroopers, the background changes. At the beginning and at the end of that scene, the street is large and full of people and beasts, but at other times, the street is small.
Continuity mistake: When Luke is in Obi-Wan's house trying Anakin's lightsaber, the coat behind him keeps appearing and disappearing. (00:32:15)
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)
Other mistake: In the first shot of the Millennium Falcon in the special edition, the top of the ship is missing its radar dish. (00:54:30)
Revealing mistake: When Greedo is threatening Han in the Cantina, there's a black object behind him. When Han shoots him, the object is smaller and some round things appear on the wall. It's visible in the screenshot of the dummy Greedo. (00:50:10)
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.