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)
Revealing mistake: After Han Solo runs into the room full of stormtroopers, you can see rubber soles under Chewbacca's feet as he follows him. (01:24:15)
Other mistake: In the scene where Luke and Leia are about to swing across the canyon inside the Death Star, Leia shoots one last time. She hits the bulkhead behind the stormtrooper on the right and he falls forward. The trooper on the left continues firing (as seen in the screencap). (01:25:25)
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)
Other mistake: After Darth Vader kills Ben, there's a shot from the docking bay towards him. Vader's lightsaber is missing its red color. [This has been fixed in the 2004 DVD, but is still valid for VHS prints.] (01:28:20)
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)
Revealing mistake: During Kenobi's final lightsaber battle with Vader, Kenobi tips his lightsaber downwards, right before a scene change. The white "glow" that should be there isn't, showing the stick-like prop the actors used in filming. There is a small white light at the tip, too. This was not fixed in the Special Edition, but it was finally fixed on the 2004 DVD. (01:31:25)
Revealing mistake: In the Death Star corridor leading to the Millennium Falcon, just before Han says "Didn't we just leave this party?" you can see Carrie Fisher and Mark Hamill's shadows on the wall as they await their cue to run in. (01:31:30)
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)
Other mistake: When the Rebel ships are heading towards the Death Star, there is a shot of the squadrons flying towards the camera. Several of the X-Wings seem to be the same model as the lead craft for they sport identical dirt and battle scars. (01:41:00)
Continuity mistake: When Luke is about to climb the ladder to get into the X-wing, there's a man fixing the ladder who starts to walk away, and another man walking under the wing and leaving. A shot later, the man by the ladder is gone, and the second guy is metres behind, though now he walks away going straight ahead. (01:43:42)
Continuity mistake: When Luke is climbing to the X-Wing, R2D2 is being brought over right next to where a guy is. He touches the robot and brings it close to him. Shot changes and the robot is away and it's being moved towards the man again. (01:43:46)
Continuity mistake: While Luke climbs the ladder to get into the X-wing's cockpit he asks R2 if the little droid is okay, then as Luke steps up he's holding his gloves in his right hand, but it cuts to the next shot as Luke leaps into the cockpit and the gloves are now suddenly grasped in his left hand. (01:43:50)
Continuity mistake: When the Gold Leader says to the Red Leader, "Red Leader, this is Gold Leader," at the start of the Battle of Yavin, the two Y-Wing fighters outside his cockpit suddenly disappear. This was fixed in the 2004 version. (01:46:05)
Continuity mistake: Towards the end of the film, the Death Star rounds the planet towards the moon in order to destroy it. The movie continually reverts back to the Death Star where a commander informs us of the time until the Death Star is in range of the rebel base. It will then show the panel with the Death Star's co-ordinates and how long until contact. However, it does not count down in minutes, it counts down in seconds. E.g the commander will say "40 minutes till contact" yet the screen will start at 40 seconds and count down, 39, 38, 37. Regardless of whether or not they use the same time system as us, the time would have run out far too quickly. (01:47:30)
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.