I saw Logopolis (of course) back in 1981 and again when it was repeated later in the year. Its biggest problem is that the pacing doesn't quite match the amount of Stuff that is Happening; the first episode in particular is alarmingly slow, episode two is incomprehensible in places, and it is not surprising that the ratings for the last two episodes were so low.
But the two million viewers who gave up on it between eps 2 and 3 were mistaken. Things I liked about it: the Watcher works really well, even though we never really find out the details of how he works. It generally looks fascinating - the nested Tardises, the streets of Logopolis. John Fraser as the Monitor is great. Nothing that the Master does actually makes sense, but it's a great debut story for Ainley who does some high-class evil laughter. Nyssa may pop out of nowhere but it's good to have her back (and out-acting Adric almost instantly). The music is super - the theme for the Watcher suggesting that he is not the Master (as Adric assumes) but something else, and that final chord sequence as it transforms into the Doctor Who theme.
The biggest problem I have with it now is that the Master's grand plan simply doesn't compute. How can he have known that the Doctor was headed for the Barnet by-pass? Or would then head for Logopolis? And how quickly will his message to the peoples of the universe reach them, indeed how will the radio telescope, sending messages at sluggish old light-speed, be able to affect the CVE in time? (And since Logopolis is out of commission, who will do this in future next time there is an entropy crisis?) We'll leave out the fact that the Third Doctor survived a much longer fall in The Paradise of Death, since that story is of dubious canonicity.
Logopolis is not one of the great regeneration stories - there are four of those, and they are The Tenth Planet, The War Games, The Caves of Androzani and Bad Wolf/The Parting of the Ways. But it is no way as bad as either Planet of the Spiders or (stretching a point as there is no regeneration) The Ultimate Foe. Good watching, with emphasis on watching rather than trying to understand what is going on.
The DVD is almost worth the cover price alone for the documentary on the transition between Doctors, "A New Body At Last", featuring interviews with Davison, Baker (as hilarious as ever) and numerous other cast and crew.
I also saw Kinda on first showing in 1982, and in some ways it is even less comprehensible than Logopolis, though in other ways it is fairly clear what is going on - giant pink snake trying to penetrate Tegan's inner recesses, and all that. It is one of Doctor Who's most successful takes on colonialism (a theme the Pertwee era consistently tried and failed with) even though that isn't really the point of the story. Wood and Miles point to the influence of Ursula Le Guin's The Word for World is Forest, and while I can see that, I think it may be a more general reflection of the ecological concerns of the day. The deep themes are laid on pretty heavily - the apple in paradise, the reflections of the "real" world in Tegan's dream, and on the whole we are shown rather than told about it. There are some impressive performances - Janet Fielding as Tegan of course, the three colonial officers (though we never find out what happened to their missing colleagues) the two Kinda women and the Trickster, which means you can almost overlook the cheapness of the sets and how wooden Adric is. Rather fascinating.
Unlike the other two stories here, I missed Snakedance first time round in 1983. It is actually good, perhaps the best Fifth Doctor story apart from The Caves of Androzani. There are two things that really make it so. First, the setting is completely convincing - this really does seem like a planet whose society extends beyond the edge of the camera's point of view. Not having the same constraints as the TV stories, the Big Finish audios have usually been much more successful at doing this, and Snakedance is a rare hit in this regard (especially for this era). The second strike in favour is the cast: Adric has been disposed of, and the irritating (and ultimately evil) young man of this story is none other than Martin Clunes, later of course one of the Men Behaving Badly. But it's unfair to the others to single him out; everyone is pretty good (again, special mention for Janet Fielding). The plot is a lot more comprehensible too, if anything almost too much like a standard Who plot, with the notable exception that rather than everyone suddenly agreeing to accept the leadership of the Doctor, who has just appeared out of nowhere, to get them through the crisis, they sensibly try and get on with it themselves and regard him as a nuisance. All very watchable.