"We used poisonous gases - and we poisoned their asses!"
Oops, sorry, wrong "Kill all humans" quote. Try again.
"Please do not throw hands at me!"
Almost perfect. It's hard to find anything wrong with this, although needless to say I'll have a go. Basically a murder mystery, with a small cast in an inescapable situation with a killer on the loose - and the butler(s) are, of course, not suspected. So Agatha Christie crossed with Isaac Asimov's "The Naked Sun" and "The Caves of Steel" (both classic SF murder mysteries involving robots).
It has some interesting characters, some nice subplots and backstory, some quite dark moments, a nicely not-too-comfy relationship between the Doctor and Leela (who have just teamed up, of course) in which she frequently knows what's going on better than he does, thanks to her hunter's instincts. The design is very nice, with those wonderful impractical-looking costumes that actually seem quite futuristic, especially when compared to jumpsuits, not to mention the face makeup that perhaps just gently hints that subconsciously humans feel inferior and want to be more like robots. The sandminer is quite well done, although it would have benefitted from being filmed at high speed and slowed down - when they're supposedly sinking at two metres per second, you can see it's a lot faster than that (having seen how huge the thing is supposed to be from the close up of the bridge from outside). Plus rocks fall very, very fast on this planet, again going by the suggested scale. (I guess the internal gravity is set to Earth normal, while outside it's far higher...
). The class structure sounds interesting but is just a throwaway line or two in the end - this and the sandminer itself both hint that the writer had read "Dune" at some point.
Plus the part in which the Doctor discusses what's now known as "Uncanny Valley" - the way people feel unease around things that seem almost like people, but subtly give the wrong body language signals - seems rather insightful. Perhaps this was old hat in 1977, but it seemed quite prophetic to me.
Also, this story has a supremely Doctorly moment:
LEELA: So what happens if the strangler is a robot?
THE DOCTOR (offhandedly): Oh, I should think it's the end of this civilisation.
Throw in the Doctor's sudden possession of a snorkel, one (count them!) use of the sonic screwdriver, some easily-constructed bombs, a fortuitous helium canister, Toos' go at being a helpless screamer (I mean, come on, she doesn't even run away, never mind kick her assailant in the, er, nuts) ... and our heroes' exit with unseemly haste - and you've more or less run out of (very minor) points that the script editor might have tweaked. This one works perfectly - a well-oiled machine, you might say.