Trivia: Luke Skywalker only uses his lightsaber for a little bit of training with the floating orb in this first film; he never actually fights with it until The Empire Strikes Back.
Trivia: The Imperial officer's uniforms were patterned after the uniforms of Nazi officers to add to their "villainous" image.
Trivia: When Alec Guinness was offered the part of Obi-Wan Kenobi he was offered about $25,000 to play the part. After reading the script he was one of the few cast members who believed that the film would be a box office hit; he negotiated a deal for 2% of the gross royalties paid to the director, George Lucas, who received one fifth of the box office takings. Guinness made over $3,000,000, making him very wealthy in his later life.
Trivia: The opening title crawl was inspired by the Flash Gordon serials, which was partly what inspired George Lucas to write Star Wars.
Trivia: Denis Lawson, who plays Wedge Antilles, is the uncle of Ewan McGregor, who plays Obi-Wan Kenobi in the prequels.
Trivia: Carrie Fisher has stated that her scenes as Princess Leia with Grand Moff Tarkin - Peter Cushing - were not easy to play. During filming, Peter, as Tarkin, would speak demeaningly to her. When the cameras stopped, he would converse with her in such a gentlemanly fashion that she found it hard to play her part against him when filming commenced again.
Trivia: Luke's line "I can't see a thing in this helmet" was not scripted. Mark Hamill said this to Harrison Ford when he thought the cameras had stopped rolling, but the filmmakers decided to leave the line in.
Trivia: C3PO was named after a post office which is located at reference C3 on a map of Lucas' hometown. R2-D2 is an abbreviation of 'Reel Two, Dialog Two'.
Trivia: During Han's conversation with Greedo, the line "Even I get boarded sometimes - do you think I had a choice?" was lifted from his conversation with Jabba that didn't make it into the original release. If you pay attention you'll notice that when he says that line the camera is on his hand unsnapping the holster of his gun, not on his face. When the Jabba scene was put into the Special Edition they left the line in both scenes, making the Jabba scene repetitive.
Trivia: Harrison Ford wasn't originally a candidate to play Han Solo, he was brought in simply to feed lines to the other auditioners. After watching Ford, George Lucas realised he was the perfect Han.
Trivia: "Vader" is Dutch for "father."
Trivia: While filming the desert scenes, Anthony Daniels' C-3PO costume kept falling apart, especially the legs. In many of the close-ups, Daniels was in costume only from the waist up. Notice as Luke and Obi-Wan pick up the damaged droid following the Sand people attack - the film cuts to the next scene with an upward vertical wipe, to avoid having to show his legs.
Trivia: When George Lucas was mixing the American Graffiti soundtrack, he numbered the reels of film starting with an R and numbered the dialog starting with a D. Sound designer Walter Murch asked George for Reel 2, Dialog 2 by saying "R2D2". George liked the way that sounded so much he integrated that into Star Wars.
Trivia: To create the sound of Darth Vader's breathing, Ben Burtt placed a small microphone in the mouthpiece of a scuba regulator, and then recorded the sound made by his breathing through the regulator.
Trivia: James Earl Jones' name did not originally appear in the ending credits. At the time of the film's release, Jones felt he hadn't done enough for the film to deserve a credit. His name was added for the film's re-release.
Trivia: The reason why C-3PO lets R2-D2 go in front of him as they enter the Skywalker's residence right after being purchased from the Jawas, is because the set guy operating R2-D2 by radio control kept on hitting C-3PO from behind and pushing him down the stairs, so in the final shot, C-3PO suddenly steps to the side, waves R2-D2 past, and the shot cuts out right before R2-D2 goes flying down the stairs.
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.