"The Witchfinders" is the first episode this season that my husband has unequivocally enjoyed, so that's a thing. He's liked most of the episodes so far but has disliked at least parts of them enough that he hasn't categorized any of them as being good. I think that he liked that the story was an adventure with little need for explanation or exposition.
One of the things that DW sometimes does that I really enjoy is encouraging me to go find out about the person or event that the episode is about. I knew enough about James I to understand everything he told Ryan (and in fact paused the viewing to explain to my husband about Mary Queen of Scots, James' succession to Elizabeth I, and the little I knew about his court, so that he could understand as well), but after the episode, I went to read about his involvement in the witch hunts of the 17th century. My husband hadn't believed that the monarch would be personally involved in hunting witches, but Wikipedia bore out that characterization, saying that James was dedicated to finding and eliminating witches and personally presided over trials - at least until a certain point, at which he started cautioning people to be careful of trusting accusations. Thus, it seems that this episode was meant in part to explain James' change of heart, which is another favorite thing of mine in DW - explaining real-life historical mysteries. (Oh, now I need to go listen to "The Kingmaker" again...)
The episode started with a relatively common scene - the witch trial of woman - which seemed to be nothing more than a historical event, but then blossomed into tracking down the causes of unexplained events in the village which had been blamed on witchcraft. It depicted the spreading hysteria well, especially in the trial of the Doctor, where even Willa, the girl the Doctor was trying to help, turned against her under pressure. I think the only part of the episode that was disappointing was the aliens themselves. Why do they always have to be slow, shambling threats? And always aching to destroy the planet once they get out?
I'd say, though, the most fascinating part of the episode was the portrayal of the witchfinders, who were doing things we find reprehensible but were absolutely convinced they were doing the Lord's work. Even Becka, while slowly being taken over by a hostile intelligence, fought against them internally and hunted witches because she truly believed that she was a good person and that if she did good works and eliminated Satan, she would be saved in the end. It was refreshing to see that she was convinced of this to the end, and not doing it because she'd turned evil.
The companions were largely irrelevant in this episode, though Ryan got quite a bit of attention from James and Graham got a cool hat. Sadly, Yaz was largely invisible. This isn't necessarily a bad thing, though - this time, the Doctor was the focus of the story, and that's fine. It was also nice to see her grump that asserting authority was a lot easier when she'd been male.
By the way, when this series first started, I hated the bass glissando in the intro to the theme. Now I really like it. I guess it just needed to grow on me.