No - I didn't understand an awful lot of what was going on, though there was still much to enjoy...
To clarify a little, I sort of followed what was going on, though a lot of the detail didn't stand up to too much scrutiny. Maybe it also didn't help that I was watching on iPlayer on my laptop, so that the dark bits were very dark indeed!
As I say, I enjoyed it immensely, but...
As has been said, we now have another "magical" ex-companion - Clara, Rose, Donna, River Song, now Bill (and probably others*) live on in hugely improbable ways. Once or twice, fair enough, but not all the bleedin' time, please...
Yet another regeneration tease. Are we to assume that all previous Doctors were a bit wet, and all you have to do to cheat death is just decide not to regenerate? I'm guessing that it's only a delay, and we get an adventure with the first Doctor and
then Capaldi will change.
I get that time moves slower, the closer you are to a black hole's event horizon, and it's a nice plot device, but I don't get how the lifts would function in such a scenario. Surely, they's either takes years to come when you pressed "call", or they'd rip themselves apart, or both?
Missy was extremely sloppy - if you're going to force your evil former self to regenerate (ie nearly kill him), don't give him enough time to get back to his Tardis and maybe make a cuppa, and oh, I don't know, pull a weapon and shoot you! Make it fast acting, FFS!
Convergent evolution of Cybermen, everywhere there are humans? Maybe, but why would they all have jug handles on their heads?
*Jack, Peri... any more?