John Nathan-Turner took over Doctor Who in the 1980s, he made it much too gay much too quickly, he alienated the kiddies (and, more to the point, their parents) and, over a period of about ten years, he squeezed the life out of it completely.
At least, that's one point of view. The alternative line, in the man's defence, would be to say that he kept the show alive long past the point when TV cultural entropy should by rights have finished it off once and for all. But perhaps we'll never know.
In any case, JN-T's first season as producer kicks off with a very slow boring "brainy" story that is overly padded with pseudo-science and backstory. It continues with a slightly more normal and enjoyable story that is almost devoid of any backstory of any sort, scientific or otherwise. (It's important to the set-up that the Doctor has been to Tigella before. But we learn precisely nothing about Meglos.) Both stories though are fairly devoid of likable characters and both end very abruptly.
Full Circle therefore feels like the first "proper" Doctor Who story of the JN-T era, with proper monsters, proper characters, a proper mystery, and so on. But it's also very much the first story of the "new" Who era that the new producer was clearly aiming for - and in fact in retrospect it's pretty much proto-NuWho. Tom and Lalla and K9 and the TARDIS are all still there from the Douglas Adams "era" (albeit with a slightly different "look"), but the show itself feels quite different, with a slicker, more self-confident (some might say slightly too self-satisfied) air.
For one thing, by Full Circle the series feels more invested in its own mythology, no longer merely raiding it for ideas or contexts (e.g. in Shada). So now Romana is being recalled to Gallifrey, we hear that the Doctor "lost" his "battle" with the Time Lords, Gallifrey looks very much as we last saw it in The Invasion of Time, and so on. It's to a writer's credit when he can move freely in another author's imaginary universe without having to warp it unnecessarily for the sake of his own story, and now suddenly for the first time the "Whoniverse" has started to feel genuine. Did the Time Lords really need a forgotten prison planet? Did they really need enemies like the Black Guardian - or even the Fendahl, for that matter? Whereas recalling Romana is definitely the sort of thing they would do, and if that leads to the TARDIS shooting off into a different pocket universe - which we later discover was probably created to trap not just an old enemy of the Time Lords but (Tolkien-style!) their Great Enemy - then so be it! The point (again, Tolkien-style!) is that world-building works when the imaginary world comes first and then the stories emerge not just in it but from it.
The other thing the series is now invested in in a way that it hasn't been for a long time is characters. Most new Doctors used to get potentially disposable male companions in their first seasons almost just to be going on with - in case the new Doctor wasn't quite "physical" enough to be the hero. (Action man Jon Pertwee was the exception that proved the rule.) But Peter Davison was destined to get a veritable team of supporting characters, one of whom was of course going to be the new young male. What was unfortunate of course was that just as he was trying to make the show more "grown-up", with the supposedly brainier scripts (and scrapping K9), JN-T screwed up by simultaneously trying to make it quite artificially more child-friendly and ending up with a slightly weird homoerotic mess. (Gays may like children's TV series - and children themselves, for that matter. But the actual children aren't necessarily going to be too impressed with visuals of men going swimming in skimpy loincloths.)
Because Alzarius's Gomorrah People are not great, by any stretch of the imagination. Why do they steal river fruit, for example, when they could presumably much more easily pick their own? It's a smaller detail than "Who is Meglos?" or even "Why exactly did the Argolins and the Foamasi go to war against each other?" But it could still have done with a bit of explaining. Adric's unlikability meanwhile is clearly deliberate. (He's supposed to be "edgy".) But we don't really see enough of his soul for it to work. He's dickish but we don't know why, but presumably because adult writers just tend to think of teenagers as being dickish. Which is definitely an odd thing to do in a TV-show supposedly aimed at "young adults"!
And the plot of course is still fairly rubbish. The characters flit to and fro as per usual, and the fact that they're now doing it by TARDIS doesn't help. Nor, for that matter, does the lamp-shading (in the story's title, no less!) of their at one point literally going round and round in circles! Where it does shine though, as science fiction as much as anything else, is with its central, character-centred sociological insight. George Baker indeed feels like the first proper actor playing the first real character we've seen in Doctor Who for quite a while.
State of Decay on the other hand feels like a throwback to an earlier era of Doctor Who, and in many ways it is. And oddly enough that's actually a Good Thing. As such, slap in the middle of this "new"-style season, it has a gloriously old-school feel to it. There's dear old Terrance on the DVD extras, spinning his old time wisdom about the changeless character of Doctor Who, and his writing is a very welcome reminder of what proper backstories used to be like. After Morbius had riffed on Frankenstein and after Fang Rock had done the same with Who Goes There?, doing an alien version of Dracula was a very logical next step for Dicks in his exploration (or exploitation, if you like) of the "classic" horror genre. And somehow his story doesn't feel out of place.
Then of course there's Warriors' Gate, which looks weird and feels weird because it's supposed to be weird, and arguably its lack of backstory is for once acceptable as part-and-parcel of its mysterious appeal. (And yes, sometimes that works, as it does in Ghost Light. And sometimes, as in The Greatest Show, it doesn't.) But then The Keeper of Traken is a genuinely appealing premise that's been butchered into fitting into the usual Doctor Who to-and-fro format, and its pseudo-science certainly can't stretch nearly far enough to cover all its Tolkien-eque elements.
The best news about Traken (albeit sad, in context) is that it's the one story in which Tom and Matthew absolutely shine together. Contrary to collective fan memories, Tom is not grumpy and aloof but (for the first time!) warm and even avuncular to his young male companion. After six years in the role, Baker was a dog that was clearly quite capable of learning new tricks. His brother-sister relationship with Sarah Jane was glorious, his attitude to Leela was explicitly teacher-pupil, and after the whacky flirty alien "thing" he had going on with Romana it's surprisingly painful in retrospect to note the beginnings of an authentic man-boy relationship that was then suddenly cut short by the Fourth Doctor's regeneration into Peter Davison.
Finally Logopolis sums up the whole season quite perfectly - visually (and aurally!) appealing, but with a huge mass of altogether unfinished confusion under the surface. Characters pop up and then become best friends with hardly any explanation, the science wouldn't cover a postage stamp, and the plot is at times quite bizarre. Never mind who the Watcher is. Why does the Doctor want to measure a police box? Why does he think landing the TARDIS in the River Thames will flush out the Master, who he knows has his own TARDIS? How does doing maths change reality, let alone stop the universe from cooling down? And why does that cooling down make people (and constellations) disappear? And how does beaming a message from a 20th century Earth radio telescope (and can one even do that?) keep a CVE open?
Nyssa and Tegan's off-on relationship with the TARDIS obviously prefigured that of the Matt Smith companions. (And why not? It worked for the Brigadier and UNIT - sort of!) But in real life it also led directly to the slightly sinister and in fact deeply unpleasant - not to mention dramatically highly questionable - decision to kill off Adric. (Once it had become the done thing for companions to go and come back whenever their actors' agents felt like it, the only way for JN-T to be sure he'd never see Matthew Waterhouse again was to have his character blown to little bits.) But was this bit of gay spite foreseen from the outset? It's difficult to say for certain. There was no "showrunner" in those days - just what Sydney Newman would have valued as a "creative tension" relationship between producer and script editor.
What is clear though is that the show's second big reboot at the beginning of the 1980s - with higher production values, more cerebral scripts, a tighter mythos and a larger cast - was superficially more radical than Jon Pertwee's "real world" colour relaunch at the beginning of the '70s. But it would turn out to be a much wobblier structure than anyone (with the possible exception of Tom himself!) could have thought at the time.