Revealing mistake: During the escape from Mos Eisley, when Han says, "They're gonna try and cut us off", he grabs the control panel in the cockpit, and the whole panel lifts off the floor. (00:53:55)
Revealing mistake: When Gold Leader enters the Death Star trench, there's a shot from his cockpit. When Luke, Wedge and Biggs enter the trench later, the same shot is used again. This can be seen from a flash of light accompanied by the sound of a shot, followed by three green laserbolts, then another flash/shot and more laserbolts.
Revealing mistake: As Princess Leia is about to undergo interrogation by the droid in her cell, the needle bears the legend "Made In England".
Revealing mistake: When Luke ignites his new lightsaber in Ben's house, the reflection of the stick used during the filming is visible on C-3PO's body. (00:33:55)
Revealing mistake: On the Death Star, before Luke and Leia try to cross the pit, Luke shoots a panel to close the door. Firstly, he shoots beside it, and secondly, after it explodes, no electronic components are visible in it.
Revealing mistake: During Darth Vader and Ben's lightsaber duel, sometimes you can see a white wire attached to Ben's lightsaber, for example after he says, "If you strike me down, I shall become more powerful than you can possibly imagine."
Revealing mistake: When Ben and Luke are transporting C3P0 after the attack of the Tusken Raiders, the arm of Anthony Daniels, the actor that plays the droid, is visible during the transition to the next shot showing Ben's house.
Revealing mistake: When Luke, Han, and Chewbacca attack the prison of the Death Star, in one shot, the end of the corridor is in a slope while it is supposed to be horizontal. (It looks to me like it's actually a flat panel painted to look like the corridor. The angle looks perfect for the opening shot of them entering the prison floor, it just looks "off" for any other angle.) This is fixed on DVD.
Revealing mistake: When Luke is first practicing with his lightsaber on the Millennium Falcon against the remote, the zapping blasts that it sends at him are in 99% of the case headed nowhere near his body, but disappear in line with it [very poor FX work] and he flinches.
Revealing mistake: When Luke opens up a light sabre for the very first time, you never once see the light reflecting from the metal of C-3PO's head (and he was swinging it quite close to the droid's head).
Revealing mistake: When the Millennium Falcon exits from hyperspace where Alderaan was, a TIE fighter follows them. There is a shot where it passes in front of the Falcon and then disappears.
Revealing mistake: Special Edition: When Luke and Obi-Wan are arriving in Mos Eisley to find a pilot, the Ronto in the background throws the Jawa riding him to the floor. When the Jawa falls to the ground a puff of dust is seen and a thud is heard, but look closely - he never actually hits the ground.
Revealing mistake: Before Darth kills Obi-Wan, he rises his saber to prepare to die and his face and hands are perfectly visible. Right before Darth kills him, there's a wide shot where his face is missing and a black object is used to hold the saber, thus revealing the actor was replaced by an empty cloak to achieve the vanishing effect.
Revealing mistake: In the scene when Luke, Han, and Chewie are in the Detention level, one of the guards walks toward Chewie. Chewie screams and punches the guard. Look carefully and you'll see the guard starts to jump backward before Chewie's hand comes in contact with his body - in fact Chewie completely misses the guard by about a foot.
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.