This episode wasn't really my cup of tea, but it had a lot going for it, and lots of positive things that we rarely see in Who episodes any more. Shame they messed it up with a couple of unnecessary moments.
This episode did have a lot of good points. Like:
+ Multiple easy Bechdel passes with different characters and different topics of conversation.
+ Multiple female secondary characters and characters of the week.
+ The presence of Vastra and Jenny WITHOUT any "lol lesbians" jokes (unless I missed it).
+ Female characters who were capable and independent, who solved problems and were brave and intelligent and generally played an important role in the story.
+ A Doctor who defends the worth of others, including (gasp) female characters.
I was all prepared to write that this episode was perfectly unoffensive, even if it was also perfectly unremarkable, plot-wise. Unfortunately, it was let down by a couple of moments. Things that didn't need to be in there for the plot, and yet appeared because... well, I guess because the writers thought they were funny?
So let's talk about the Doctor and Jenny. Throughout most of the episode, Jenny was an interesting, brave and capable character in her own right. Unfortunately, we got treated to two less respectful moments involving her. In the first, the Doctor kisses her quite forcefully to celebrate his recovery, and when she slaps him, he laughs and says that he enjoyed that too. So we have the Doctor "snogging" a woman who 1) is in a committed relationship, 2) is a lesbian, and 3) gave no signal that she'd be interested. And although she slapped him, the slap seemed part of the joke as well. Her protest was all part of the fun of the moment, or so we seem to be expected to believe. It wasn't saying that the Doctor overstepped a line and should not act that way, but that it was all good, enjoyable fun, from the kiss to the slap itself. Her protest wasn't taken seriously. It was part of the moment that the Doctor wanted to create. She didn't really protest, and if she did... well, silly her.
The next moment was shorter and even more unnecessary. When Jenny takes off her dress to reveal a more Black Widow-esque outfit so that she can fight, the Doctor's expression is somehow both flustered and leery. "Oh how hilarious," we must think. "The Doctor's all hot and bothered by Jenny." But the moment dehumanizes Jenny and takes her agency away from her. She isn't being a kickass figure in that moment, fighting to save them. She's become something more sexualised, something to be looked at and appreciated physically, rather than an important individual in her own right. In any other context, it'd be something that could easily be glossed over. But considering the fact that it's a show watched by little girls, the fact that they keep trying to make the Doctor into some kind of playboy with PG-versions of Game of Thrones scenes, and all the sexist jokes that the Doctor has made recently... it's harder to shove it aside and pretend it didn't happen.
And it's all so unnecessary. The plot isn't built around this kind of sexism. In all of its other elements, this episode was actually pretty fantastic for female characters. So why throw these things? Why add these casual little asides? It's almost more depressing that they decided these were good, funny additions.