Another trigger warning: An obvious non!Trump character.
- I think Not!Trump is uncomfortable as a character, a tonal misstep, and arguably a problem for later in the season. At this point we're past fictional references and so on; things have gone too bad in RL in too serious ways for that. But that's a personal feeling, and I can understand the opposite stance.
- I liked it when the Doctor asked somebody's friend permission to break into their apartment; it's the sort of thing recent regenerations have tended to not care about, but I think matters. (Of course, when Stuff Gets Going she's as likely to be deterred by KEEP OUT signs as any other Doctor.)
- I loved how the gang decided to travel with the Doctor before she asked, how careful she was about making them understand the risk (not that they can, not really, but that's because the out there is so much weirder than what they've seen so far; nobody could, not even the Doctor, back before she stole the TARDIS), and then how openly happy she was about it.
Also: I don't think Yaz/Thirteen will become a canon thing, but it would certainly be nicely straightforward. Eleven/Clara and Twelve/Clara are both examples of how... fraught Doctor/Companion relationships can be (my reading of canon being that their mutual obsession was, if possibly not healthy, certainly romantic in that not-necessarily-sane way; whether they ever had sex is as irrelevant as whether Kirk and Spock, or Hannibal and Will for that matter, ever did), but right now they are both sweet, kind, bright people who think the world of each other in a rather uncomplicated way, so at least there's a very unforced path for fanon there.
That said, we don't know Yaz's sexual orientation &madsh; although her mother thought it possible that she could be dating the Doctor, and her sister that she could be dating Ryan — and we don't know the Doctor's either — in fact, I'm thinking the Doctor isn't quite sure yet, either, although her answer to whether she and Yaz were dating was "I don't think so. Are we?" (in a puzzled rather than flirty manner, I hasten to add as I see how this looks on the screen).