I had been afraid going into this story that it was going to be a political statement on Partition Day and relations between religions, and I was pleasantly surprised to be proven wrong. Note that the episode couldn't not comment on these topics, but it did so within the story itself. Same goes for the history lesson: as an American viewer, I had little knowledge of the historic day in British and Indian/Pakistani history, but the episode told us everything we needed to know without a long history lecture. The deft handling of the exposition in itself, in my eyes, made this story far more successful than the previous history-based ("Rosa") and science-based ("Arachnids in the UK") episodes.
The opening was a little weak, in my opinion, as I didn't find Yaz's curiosity about the watch and her nan's secrets a particularly good reason to take her back to spy on her. However, it was good enough and better than the alternative (the TARDIS landing randomly and the crew finding themselves in the right place at the right time to spy on one of the companion's relatives), and honestly, the episode took off from there. It started with a great puzzle - why are alien assassins after people in this backwater village? - but progressed to the human story of two lovers caught up in the flood of greater events.
Umbreen and Prem were the focus of the story, of course, and they were both strong characters, fighting for their wedding against almost everyone else involved. You can really see the woman Umbreen was in Yaz's nan from the first scene, and the young version carries that through the story. However, I think that Manish is the character that most people will overlook, simply because he was so objectionable. He put a face to the violence of the day, showing how people who we might otherwise think of as intelligent and compassionate (I'm sure they gave him the glasses to underscore that) end up believing ideas and committing actions he might otherwise consider reprehensible. This is one of the things that failed for me in "Rosa", that the time-traveling villain and the white citizens of Montgomery were faceless racists, one-dimensional and unimportant, and I was happy to see the real villain developed so well here.
And while we're talking about villains, the Thijarians turned out to not be villains at all! This is a rarity in DW. They did a good job of making them look like villains and then having a real reason to be where they were. I do wonder, though, if the Thijarians and the Testimony get into fights over who gets to take the person.
Another rarity in DW: the Doctor loses. She isn't able to make everything come out all right for the good guys in the end. Prem dies and Umbreen loses everything, and this is right for the story.
I also really enjoyed the Doctor's little quip, "I never got to do this kind of stuff when I was a man," and her attempt to cover up what she said. As I've always felt, Time Lords shouldn't have any issue with changing gender, but certainly they would notice when gender-restricted things become open to them.
I think the one weakness in this story was Yaz herself. This episode should have developed her character further, but as the TARDIS crew really were just observers of the event and were trying not to interfere, she didn't get that opportunity. I will note that she does not insist on trying to save Prem - doesn't even suggest it - showing her maturity and strength of character.
The bottom line is that the writing and pacing of this story was fantastic, and considering that this was the first episode to not be written by Chibnall, it's making me nervous about the future of this era of the show. I've liked Chibnall's writing in the past - "42" is one of my favorite episodes, and the character work he did in Broadchurch was stellar - but his work so far this season has been disappointing (not bad, just not brilliant). We still have four episodes and a special to go, so I suppose we'll just have to wait and see.