Continuity mistake: When the Jawas are walking toward Luke to take the damaged droid, there's no more smoke coming from it but in the following shot, there's a lot of smoke. (00:19:18)
Other mistake: Before Uncle Owen yells for Luke, if you look very closely, a fly can be seen on the lens (best seen on the special edition release). The fly was removed in the 2019 release.
Other mistake: When the stormtroopers break into the control room, the stormtrooper on the right of the screen hits his head on the door frame. On the DVD release they've added a thump when he hits it. (01:18:55)
Visible crew/equipment: When Luke, Han, Leia, and Chewbacca are in the trash compactor, there is a shot of Chewbacca knocking on the door. If you look to the right side of him, you can see the reflection of the blue stage lights on the metal part of the wall.
Continuity mistake: When the Gold Leader says to the Red Leader, "Red Leader, this is Gold Leader," at the start of the Battle of Yavin, the two Y-Wing fighters outside his cockpit suddenly disappear. This was fixed in the 2004 version. (01:46:05)
Continuity mistake: When R2-D2 is hiding from the Sand People, he is standing in front of a rock. When he comes out, the rock disappears. 2011 Blu-ray and 2019 4K.
Continuity mistake: DVD and Blu-ray only: When Darth Vader and Obi-Wan are dueling on the Death Star, all shots of Obi-Wan's lightsaber are blue. But in two shots, his lightsaber changes to purple. This was fixed on the 4K release.
Other mistake: After Darth Vader kills Ben, there's a shot from the docking bay towards him. Vader's lightsaber is missing its red color. [This has been fixed in the 2004 DVD, but is still valid for VHS prints.] (01:28:20)
Continuity mistake: When Darth Vader and Ben are fighting, Darth's chestplate is on backwards and the belt "buckle" is as well. It appears that the entire shot was reversed. (01:26:20 - 01:27:15)
Continuity mistake: After the Stormtrooper tells Darth Vader the Death Star plans are not in the main computer, when Vader lifts the Rebel off his feet by his throat as the Rebel tells him they intercepted no transmissions, take note of the leg plates on the Stormtrooper to Vader's right. In the wide shot, the Stormtrooper's left leg armor does not have the knee protector plate (it looks as if it's at his right knee because the extra switched them), but in the next closeup the knee plate appears at his left knee, as it should be. The trooper also appears to go from right handed to left handed weapon carry. (00:05:40)
Revealing mistake: In the scene at the end of the very first battle, where Imperial troops have just taken control of Princess Leia's rebel ship, Darth Vader breaks the neck of the Captain Antilles and tosses his body to the wall. The "dead" Captain puts up both of his hands to avoid slamming his face into the wall. (00:05:40)
Other mistake: In the scene where Luke and Leia are about to swing across the canyon inside the Death Star, Leia shoots one last time. She hits the bulkhead behind the stormtrooper on the right and he falls forward. The trooper on the left continues firing (as seen in the screencap). (01:25:25)
Visible crew/equipment: At the beginning when R2-D2 is in the escape pod and C-3PO is arguing with him there is a shot of C-3PO from the side and you can see the reflection of the camera in his head.
Revealing mistake: When the Tusken Raiders are seen raiding Luke's speeder, you can actually see the wheels or at least whatever is holding it up off the ground. (00:28:10)
Revealing mistake: On the Jawas' transporter, when R2D2 looks around in one of the shots, you can very clearly see the actor, Kenny Baker, inside through his eye hole.
Visible crew/equipment: Just after the Falcon takes off from Mos Eisley, there's a shot of the Falcon with Star Destroyers chasing. The next shot is of Han Solo alone in the cockpit. Watch carefully behind him in the doorway, and you'll see the shoulder of a man in a green shirt quickly move out of shot. In fact, this is Alec Guinness and the shot is an insert from the slightly later scene where Obi-Wan and Luke are in the cockpit. After Han tells them to strap in for their jump to light speed, this shot is seen again with the pair retreating down the ship's corridor. The earlier shot reuses the final frames of the later footage and the edge of Guinness' shoulder, his costume reflecting the green set lights, is visible. (01:01:05)
Visible crew/equipment: In the original widescreen version, during a long shot of a loading bay in the Death Star, you can see a crew member walk just into shot on one side of the screen, stop, look up, and back out again.
Continuity mistake: When Obi-wan and Luke are watching the hologram of Princess Leia projected onto a small table, the objects on the table change position and number in each shot. (00:33:35)
Continuity mistake: After Luke gets pulled underwater in the trash compactor, he is shown with a piece of garbage on his forehead in one shot. In the next shot his forehead is clean, but in the following shot, the piece of garbage is back again. (01:21:35)
Revealing mistake: In the Death Star corridor leading to the Millennium Falcon, just before Han says "Didn't we just leave this party?" you can see Carrie Fisher and Mark Hamill's shadows on the wall as they await their cue to run in. (01:31:30)
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.