There have been other "this is my reality, my rules" scenarios before (and since the original one for which this is a 'rematch'), they do like to chuck in pocket-universes, 'dream'-realities, elder-gods-masquerading-as-mundane stuff, etc, on occasion, though perhaps this one is more unbounded (except for 'the rules'[1]). Perhaps Q-like?
Reproduction, though I think never seen (conception and/or birth), actually seems to have been 'normally' handled by "when a Time Lord[2][2b]and a Time Lady[2][2b] love each very much", of whatever variety we might imagine most of the generally humaniform races of scifi reproduce[3]. We learn that The Doctor is a bit of an exception (as often), but The Master was a fellow child to stare into the Eye Of Harmony/whatever. And
this is stated to have never happened before (as indeed might not the whole Ten-A 'metacrisis' - Ten/Fourteen really likes to give of himself). The reverse (sort of) happened with The Watcher in the Four->Five sequence, but that's probably now considered as Early Installment Weirdness, by reboot-standards. Though, interestingly, Thirteen->Fourteen otherwise uniquely did the same as One->Two in coming with an inherent costume change, rather than requiring a wardrobe-run (especially for Eight) to work out what their new body likes (and Fourteen+/Fifteen clearly had to split Fourteen's clothes).
Too early to be sure about Fifteen. He has the energy. Bouncing interactions around, to prove it (in-universe he gets approval from the various Doctorologists present). I think he'll have his fans and detractors, as with followed all prior cast-changes, but I'll probably enjoy seeing his character work out.
Doogie Howser, MD! Long time, no see... Three accents ('faux', 'real' and 'showman'; presumably theatricaly-inspired, studied and close-to-normal for the actor).
It took until the end-credits to understand the weather/origins comment. So, he's anglo-indian. Honestly, his 'duskiness' just escaped me. But then I was initially confused about attitudes towards Meghan Markle, when all that fuss started.
I don't think UNIT's building was so much of a Stark Tower(+ elements of SHIELD) clone, last time. Marvel/Disney influence?
I thought she was going to slap him, nice (but in hindsight obvious) misdirection.
Postcodes applying to that era of London? (1959 Norwich to 1974 UK-wide, at least to "AB1 2CD"ish level of differentiation.) Ok, so an overlay of the present-day system works when a TARDIS can appreciate any system that is contemporaneously most convenient for a given Earth-organisation. (Must rewatch, check if that's the valid contemporary one, and then historically correct. Rather than a fake/reserved-for-fiction one.)
That big gun... A bit basic in the long-distance CGI, when expecting something of a Christmas Invasion component. (Though it had to be no more than a single-manned 'AA gun' thing to work with what happens next.) But given a 'gunlike glowy ammoclip' in the closeup, to continue that analogy. Yet it's a beam-weapon... wrong aesthetic, really. Glass discs/rings around light-effect barrel should be the order of the day. And far more actual greebles/nurnies (a bit too 'boxlike', though of course you can also go to far...)
Among the dead (Kate making sure to know the details of her own Redshirts/by-kills, aside), there's the
A call-back to the Master's ring (a call-back itself to Ming The Merciless/etc?), so who is the new Miss Trefusis? But clearly leads to scope for new Missy/Master involvement.
[1] Do let me know what the rules of 'catch' are, though. I'm sure I couldn't be sure what the ur-rule for the ur-game, as depicted, vis-a-vis deliberate or accidental 'wide's that can never be caught. Clearly there's nothing against Bodyline, either.
[2] At least at the moment concerned. And for the moment concerned. Apart from a lot of problems with potential paradoxen (which we know a Tardis can be equipped to handle, by one so determined, though that's one humungous 'sex aid' just to make even the foreplay less likely to attract a Time Reaver audience!) there's potentially nothing to stop anything up to and including a full-blown All You Zombies 'family' relationship from happening.
[2b] And possibly insert just "Gallifrean" in here, there being non-'Lord'ly citizens of the race.
[3] The "Knee Jerk Alien", (somewhat distracted by hard 'knee' contact on Rura Penthe, Star Trek: the Undiscovered Country) might be one exception, but rarely are such issues addressed directly in 'rubber foreheaded alien' races. I mean, the Alien race (the drones/immature queens still particularly humaniform when their host is human) is actually hive/colony/parasitic-insect in nature and various Energy Beings with human forms might have various options. In the Whoniverse, there's Daleks (and Sontarans, and others) grown in tanks, presumably the tree-race (e.g. Jabe, on Platform One,
The End Of The World) are more true to their biological origin, and the whole thing of the Adipose (somewhat humaniform in a baby-like way when young, whatever they are when adult) will be different, amongst other exceptions, but it's mostly left unsaid/handwaved/not subject to discussion.