The animation here is quite good -- a significant improvement over The Reign of Terror by the same people, as the editing here isn't nearly as distracting. It'll never replace the real thing, but it sure beats peering at telesnaps.
It's an entertaining first episode; there's some fun larking about in spacesuits on the moon before the Doctor and his companions head inside the eponymous moonbase, the crew of which is suffering from a mysterious illness that seems to strike at random. Somewhat surprisingly, the Doctor isn't instantly under suspicion for this, and he gets to spend the first episode filling in the audience on the basic facts: "Every school kid knows about the Gravitron in there," Hobson says. "Ah, yes," the Doctor replies, "it must be about the year 2050, Ben." It's actually 2070, but only twenty years off isn't bad. And it turns out that this is another remote base crewed by an international staff (although, as About Time 2 points out, with Americans curiously absent) -- at which point we note that writer Kit Pedler's last story was The Tenth Planet, which also had an isolated international base and Cybermen.
To his credit, director Morris Barry seems to be holding back the big reveal (based on both the telesnaps and the animation), showing us hints of Cybermen (including, memorably, a jug-handled shadow) without giving away the whole thing until the cliffhanger -- at which point we see that the Cybermen have been massively redesigned. They're a lot sleeker than the Tenth Planet version, with solid metal faces, three-fingered gloves, and cables running along their limbs (actually this was present in the originals too, but it took a bit of faith to see them as such).
Episode 2 has always existed in the archives, so we're back to the real thing. It becomes clear that the moonbase is under attack by the Cybermen for some reason, but via stealth rather than force -- which means that Hobson, the leader of the base, refuses to believe Polly's story that there are Cybermen around. "There were Cybermen, every child knows that, but they were all destroyed ages ago." Instead Hobson's finally decided that the Doctor and company are worthy of suspicion for this inexplicable disease, but the Doctor denies being responsible and declares his intention to help find the real cause, because "there are some corners of the universe which have bred the most terrible things. Things which act against everything that we believe in. They must be fought" -- as good a summation of this phase of the show as any other (and a significant departure from the ethics of the show when it began).
So to help find the cause he naturally causes as much havoc as he can, interrupting people while they're working by taking their shoes off and snipping bits of fabric from their clothing. Yet he can't find any cause, and it's only pure chance that he learns it's the sugar that it's infected -- because apparently "pok[ing] into everything" didn't include the sugar. (This isn't the only bit of silliness on display, by the way; we also learn the fact that the Cybermen can seal up a giant hole in the side of the moonbase with a few sacks of food, but when they go in and out there's a momentary drop in air pressure.)
And then, because Hobson didn't believe the stories about Cybermen, that means that this episode's cliffhanger also gets to be a dramatic reveal of a Cyberman. You start to get the feeling that maybe the current production team don't have that much faith in their audience's ability to notice they're getting the same thing twice...
33 Public service announcement: the region 1 version of The Moonbase was mastered incorrectly as progressive video, accidentally eliminating the VidFIRE process that gives them that "studio video" look, as well as making the episodes run about a minute longer than they're supposed to. If you care about such things (and you should), the region 2 DVD doesn't have this problem.
34 Unlike the Cybermen from The Tomb of the Cybermen, the Moonbase Cybermen don't have cables coming out of the bottom of their chest unit. And yes, I'm the sort of person who knows these things.