...I was under the impression that the production history of the show was:
(1) A 13-episode first series was produced, with "Once Upon A Time" as the intended cliffhanger. That episode was shot sixth to accommodate shooting Leo McKern's episodes back-to-back. After this run, George Markstein (script editor) had a falling out with McGoohan, and did not return for the second series.
(2) A second series was produced, which consisted of only four episodes because the network cancelled the series prematurely, forcing McGoohan to rush the scripting, filming, and post-production of "Fall Out." These episodes were not filmed using the Portmeirion location.
Okay, I did some research, and apparently this is a fan myth that's rooted in some degree of truth. Yes, there were two separate production cycles, one with 13 episodes filmed from September 1966 to April 1967 and one with 4 episodes filmed from August 1967 to January 1968. But no, the second cycle was not a second 13-episode season that was cancelled prematurely.
http://numbersixwasinnocent.blogspot.com/2009/09/mcgoohan-on-my-mind-number-of-beast-or.html
The main contention of prisoner fan books concerns the reasons for number of episodes being 17.... They have derived a notion that because a block of 13 episodes formed the first part of the production process that there was an intention to have a further 13 and perhaps even another 13 after that. McGoohan, in 1977, had told them his truth, but as was typical of the cult fans, they simply did not believe him....
In fact, despite all the fan-club rumour-mongering and their unattributable reports of off-stage whispering, there is clear and irrefutable evidence that the number of episodes had been confirmed at 17 within 1966. In February 1967 an American newspaper article quotes Mike Dann as having purchased at least 17 episodes of the new McGoohan show called The Prisoner. From the tenses implied within the quotes it is evident that Dann had first confirmed the deal before a single episode had been shot.
...
Before the August 1967 second shooting schedule ever began the number of 17 was reiterated as a certainty, with McGoohan’s clear statement that he would be making only four more episodes.
There's no question that it was McGoohan's own choice to make it a limited series. He didn't like the idea of dragging out a concept indefinitely, and even 17 episodes was more than he wanted and the absolute maximum he would agree to. The network absolutely did not "cancel" the series -- McGoohan ended it on his own terms.
Galactica 1980 is generally considered to be a separate spin-off show rather than a seaQuest-style overhaul within an ongoing series.
Not only considered to be, but definitely was. Battlestar Galactica was cancelled, period. Its cast and crew moved on to other projects. But ABC had lost a lot of money on the show and pressured Larson to make a sequel series that would amortize the cost of the sets, props, costumes, and stock footage while being shot in a more inexpensive Earthbound setting. Since most of the original show's creators and stars had gone, G80's production had few people in common with the original. It was definitely a separate series, a sequel rather than a continuation. (Not to mention a soft reboot, because the original was pretty clearly in Earth's future, and the sequel series supposedly set decades later was in Earth's present.)
The basis for the confusion is that G80 was folded into BSG's rerun-syndication package and the episode had their title cards changed to read Battlestar Galactica, creating the impression that it was a continuation of the same series.
On the other hand:
Its been awhile since I've seen it but does The New Original Wonder Woman count as a one season show? It was set during WWII and aired on a different network from The New Adventures of Wonder Woman.
That's definitely a single continuous series. Despite the title, network, and format changes, it was a continuing production with largely the same cast and crew. ABC was hesitant about renewing the show because of its period setting, so CBS swooped in and offered the producers a pickup if they'd move it to a contemporary setting and a more standard '70s adventure format.