The obvious thing to focus on with Empress of Mars is that it sounds great in synopsis. Victorian soldiers on the red planet? Yes, excellent! Exactly the sort of thing Doctor Who excels at, taking something familiar and plonking it into a setting we've never seen it in and don't associate it with. Space-faring, red tunic-ed, pith helmet-ed Victorian soliders are wonderful as an image.
The trouble is that this is prime time television and it needs to be more than just a wonderful image to be worth watching. And, sadly, that's where things fall apart for Empress. Because it's written by Mark Gatiss. I don't dislike Gatiss's Who work but he's not a writer that makes you think he'll do anything worthwhile with an interesting concept like Victorians claiming Mars for the Empire. He's more a "safe pair of hands who can deliver a workable script on time and to budget" type. Doctor Who needs writers like that, because it's difficult and expensive to make. It's just a shame that they sometimes get paired up with ideas that warrant a little more flourish.
Gatiss brought an additional problem to this: his adoration of the subject matter. To a large certain extent a love of the subject you're writing about is a good thing. It comes across in the writing and generally improves things because the writer is that extra bit invested. But a Doctor Who script that sees Victorians invading somewhere should really at least touch on the evils of imperialism, even if that somewhere is Mars. It didn't need to be a focus. We didn't need the Doctor laying into Victorian values. But some sort of acknowledgment of the matter would have been nice, and we didn't get it because Gatiss is far too invested in this era to knock it in that way.
The other object of his affection was the Ice Warriors. The motivations for the two main Ice Warrior characters, Friday1 and Iraxxa2, were all over the place. Friday started out the episode having used the Brits to get back to Mars to uncover his people (which would have left them stranded). He ended the episode disobeying the supreme leader of his people, who was of royal blood which is totes super important to the proud and noble Ice Warriors, to defend the Brits. This after they'd turned him into their butler. Meanwhile Iraxxa went from wanting to revive her race (or at least a hive's worth of it) to starting an interplanetary war within about two minutes. They were there to serve the plot rather than be believable characters in their own right. Kind of an odd thing for the Ice Warriors' biggest fan to write.
I shan't even get into the entirely unnecessary and utterly self-indulgent cameo from giant talking penis Alpha Centauri except to say that it was Gatiss at his absolute worst.
All of which makes it sound like this episode was bad. That's not the case. Capaldi and Mackie did what they could with average material. The supporting cast were good. The body-scrunching effect from the Ice Warrior guns was great. The bookending of the "God save the queen" message was a nice touch (if a little Moffat Lite). Nardole wasn't in it much. It was for the most part a perfectly serviceable episode of Doctor Who. It's just a shame it couldn't achieve more when it had such a strong central image to work with. Which is something I thought I'd stopped writing about series ten. Apparently I haven't.
1 Strange that despite his clear and stated love of the Ice Warriors Gatiss never bothered to establish this character's actual name, sticking with the one given to him by British soldiers throughout. See what I mean about him being that bit too invested in the Victorian era?
2 You know she's alien because she has a double X in her name. Nice one, Mark! Never change.