Continuity mistake: When Vader picks up the rebel in a choke grip, the legs of the stormtrooper in the doorway behind them are apart. In the shot of the rebel's feet, the trooper's legs are together. When Vader tosses the dead rebel into the wall, the trooper's legs are apart again.
Continuity mistake: When Luke and his aunt and uncle are eating at the table, the white drink pitcher alternates from being next to Luke's cup to being across the table throughout the scene.
Continuity mistake: When Aunt Beru speaks to Luke about buying droids, there are many shrubs besides Luke. In the next shot, they are gone.
Continuity mistake: Special Edition: Luke, accompanied by the droids and Obi Wan, is in the speeder heading into Mos Eisley, but just as the shot ends it looks like they're about to run over a few pedestrians... they're heading full speed at a group of three or four people just when the camera angle changes. (00:40:50)
Continuity mistake: When Vader tells Tarkin that Obi-Wan is in the Death Star, as Tarkin says, "The Jedi are extinct." he is standing between two chairs. In the next shot, he is standing behind one of the chairs. The distance between some of the chairs around the conference table changes during the scene as well.
Continuity mistake: Special Edition: When Han is talking to Jabba the Hutt, as Jabba says, "Why did you fry poor Greedo?", the man standing to his left is pointing a blaster towards Han. In the next shot, the man is no longer pointing the blaster at him. (00:51:00)
Continuity mistake: When Vader is strangling the Rebel aboard the blockade runner, the Rebel's hands keep changing position between shots, as he tries in vain to loosen Vader's grip.
Continuity mistake: After Obi-wan saves Luke from the sand people, there is a shot of him sitting on a rock and his white robe is visible, then there is a close-up and he says "I don't seem to remember owning a droid" and his robe is not visible. (00:30:20)
Continuity mistake: In the control room when Obi Wan decides to leave them, the red beam on the radar behind him points down. When it cuts it is suddenly pointing up. It couldn't have moved that fast.
Continuity mistake: When Luke is outside of the farm seaching for R2D2 with his binoculars, C3PO is not visible in them even when Luke turns in front of him.
Continuity mistake: In the opening shot of the movie, sunlight strikes Tatooine from above, but hitting the two moons from the left. (00:02:00)
Continuity mistake: When Luke is eating with his aunt and uncle, he takes a sip of blue milk, and then lowers his cup twice.
Continuity mistake: When R2D2 has finished showing Leia's holo-message to Luke, C3P0 says something like "he has become a bit eccentric." When he says that, there is a wire coming from his belly. It was not there before or after.
Continuity mistake: When Luke and the others are trapped in the detention corridor, there are some black marks on his stormtrooper armour, on his chest, which weren't there before. These marks change slightly between shots, and in the wideshots they are missing.
Continuity mistake: When R2 and 3PO are walking in the desert look at the sun's reflection on C-3PO's head throughout the shots. It keeps changing places.
Continuity mistake: In two shots of Chewbacca in the beginning of the trash compactor sequence, there's a little area of blue paint on the right side of the hatch. For the rest, the blue spot is missing. (01:16:00)
Continuity mistake: Widescreen version: In the trash compactor, in the scene where Han says, "One thing's for sure, we're all going to be a lot thinner," the pole used to stop the compactor is leaning on the wall in different angles between the wide shot and the close-ups.
Continuity mistake: As R2-D2 is rolling through the canyon, he's on a smooth part of the land. He then stops and looks around. When he starts moving again, the terrain has changed and is now full of rocks and pebbles. (00:11:20)
Continuity mistake: When R2D2 and C3PO escape from the Blockade runner, the rate at which the escape pod turns when seen from the outside does not correspond with what we see from inside.
Continuity mistake: Special Edition: When Han is talking to Jabba the Hutt, when Jabba begins to says, "What if everyone who smuggled for me dropped their cargo at the first sign of an Imperial starship?", Chewbacca can be seen walking behind them. In the next shot, he is suddenly walking next to a wall that was nowhere near him in the previous shot. In the following shot, he is back to his original position. (00:51:00)
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.