Continuity mistake: In the scene where R2-D2 is rolling down a path on Tatooine, under the eyes of scavenging Jawas, the path he is traveling on can be seen to end several feet in front of R2, and beyond it is a rough, rocky surface that R2-D2's wheels could not possibly traverse. In the next shot, R2 is rolling down a suddenly extended (or perhaps the same?) path towards capture.
Revealing mistake: When Darth Vader releases the admiral and he slumps on the desk, the force of the impact makes the whole set wobble.
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: When the Millennium Falcon is attracted to the Death Star, there is a frontal view of it. At the end of that shot, the sky under the ship becomes suddenly bright and you can see the stick used to move it.
Continuity mistake: When Luke and Obi Wan arrive at the Cantina, watch the Jawas sitting outside the Cantina. They're initially sitting in a shadow, but when Luke and Obi-Wan walk towards them, they're suddenly in broad daylight. (00:42:45)
Continuity mistake: When Han, Luke and Leia are trapped in the corridor in the detention block, a loose piece of hair on Leia's forehead keeps disappearing and reappearing between shots.
Continuity mistake: When you first see the Millennium Falcon, it is in the hangar. If you look close enough, you can see that only half of the ship is there. This is because it was too expensive to build a full-scale model.
Continuity mistake: When Luke comes to eat dinner with his aunt and uncle, as the shot ends, he has just sat down by the table, but in the next shot, he's already helping himself to the food. (00:22:45)
Continuity mistake: When Han Solo and Luke Skywalker escort Chewbacca up to the Cell Bay to rescue Leia they are still wearing the stolen Stormtrooper uniforms, including white boots. Yet after they escape the trash compactor they are back in the boots they were wearing when they escaped Tatooine. While we can believe the rest of their outfit can fit under a Stormtrooper uniform, the boots wouldn't.
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 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.
Deliberate mistake: When Obi Wan deactivates the Death Star's force field, there's an electronic gauge going down and a sign in clear English with the word POWER - as we've seen in shuttles and other places, they don't use English. The studio decided it was better to show "power" and "tractor beam" in English so that the audience would know what Obi-Wan was doing. The lettering we see in Jedi doesn't really affect the plot, so it doesn't need to be English. Still doesn't really fit though. This is fixed on the DVD.
Visible crew/equipment: After the heroes have escaped the trash compactor and we see them arguing outside of it. As they walk away and Han says "No reward is worth this," the shadow of the camera covers his whole face.
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)
Other mistake: In the beginning of the movie, when Leia is uploading a message into R2, we can see C3PO looking for R2. When they show C3PO, there are rebel soldiers behind him, running through the corridor, being shot at and falling down. If you look closely, you can see a black stripe vertically running down in the middle of the doorway.
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)
Other mistake: After the escape from the Death Star, the first TIE apparently blows up, but behind the explosion we can see it still intact.
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.