Deliberate mistake: After the Tusken Raider has attacked Luke, he raises his stick over his head and shouts. The movement of his clothing is extremely unnatural. During the editing, they put the same footage forward, then backward many times, to add emphasis to his movements, but it looks decidedly odd. (00:29:02)
Continuity mistake: In the scenes in the conference room in the Death Star, the black hemisphere on the conference table changes position between shots.
Continuity mistake: During the binary sunset, the two suns are closer together in the close-up than in the wide shot. There is also a cloud and a mountain in front of the lower of the suns, which weren't there in the wide shot.
Revealing mistake: In the Death Star, when Han is screaming and chasing some stormtroopers and enters a room full of them, some are cardboard.
Continuity mistake: When the Jawas arrive to sell the droids, Luke walks over to R5-D4 (the "R2 unit with a bad motivator"), and the droid is standing in front of R2-D2 on Artoo's left. In the next shot, the two droids are standing perfectly next to each other, and there are several Jawas around them that weren't there in the previous shot.
Revealing mistake: On the Death Star when C-3PO makes the announcement that he and R2 should join the others back on the Millennium Falcon, as R2 begins to move, the poor droid's right leg becomes rooted and begins to pull away from its socket.
Continuity mistake: When Luke is eating with his uncle and aunt, the cup he's drinking from keeps switching hands.
Audio problem: When Vader and Tarkin learn that Leia has lied about the location of the Rebel base, we hear Darth say "I told you she would never consciously betray the rebellion." There is a pause and Vader continues to move. An obvious dubbing error.
Continuity mistake: The first time Chewie gets into the cockpit of the Millennium Falcon, he hits his head on a small set of dice. They aren't seen in subsequent shots, nor are they seen in the rest of the trilogy.
Continuity mistake: In the Detention Block, Han and Luke are in their stormtrooper outfits and are firing at the enemy. They go to a shot of Han then to Luke. Luke's white shoulder pads of his stormtrooper outfit are clearly missing, and you can see a black undergarment. They then go back to Han and then back to Luke again, where the shoulder pads are now back. (01:15:20)
Revealing mistake: After they free Princess Leia, other stormtroopers make the door explode to enter the detention room. You can see that the door is pre-cut.
Continuity mistake: When Han and Luke (disguised as stormtroopers), and the "captured" Chewbacca are waiting for a lift in the Death Star, an officer wearing a grey shirt walks by, which changes to an officer wearing a black shirt in the next shot. Widescreen version only.
Continuity mistake: In the scene where stormtroopers are firing at the Millennium Falcon as it leaves Mos Eisley Spaceport, watch the trooper on the far left. After he is shot he begins to fall, then suddenly he's standing again in the next shot, where he begins his fall again. This happens two or three more times, this falling and straightening.
Revealing mistake: After Luke orders a drink in the Cantina, there's a shot of two purple-skinned aliens. One of them has big, purple, alien hands, but the other one is wearing white gloves over human hands.
Revealing mistake: When Han shoots a stormtrooper and runs after the rest of them, the stormtrooper he shot moves his leg out of the way so Han won't trip.
Revealing mistake: When Luke and Leia are trying to escape the Death Star and they are stopped in front of the chasm, the stormtroopers shoots on the door, but you can see the pyrotechnic charges and the explosions are not where the laser touches the door.
Continuity mistake: In the end scene, when they blow up the Death Star, whether the camera is on the Ties or X-wings, the enemy is never visible in front or behind them.
Continuity mistake: In the wide screen version, after Luke, Han, Chewy, Obi-Wan and the droids come out of the hidden cargo bins in the Falcon, Obi-Wan says "Who's the more foolish, the fool or the fool that follows him." Then he tries to lift himself out of the bin...it looks as if he doesn't quite have the strength to do it - he puts his arms on the side, exerts a bit of pressure, and waits for the cut.
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.
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.