As for other things about this episode...
Re: Osgood's death.
Pointless. I liked her. I can only hope that was Zygon Osgood; maybe they've been trading off days and this was Zygood's day (and day to die.) Though if that were the case, you'd think that Zygood would have undisguised itself and surprised the hell out of Missy... Also, those soldiers were apparently UTTERLY useless, to the point I suspect that they may have been holograms under Missy's control all along. Seriously, they were BEHIND her, and didn't notice her picking the lock on her handcuffs? (And for that matter, why did they restrain her with handcuffs, and not zip-ties? And why didn't they SEARCH HER when they had her restrained? USELESS!)
Why didn't the DOCTOR order someone to search and make absolutely sure that Missy was very, very thoroughly restrained? He of all people should know how crafty and canny she is. He was the President of the World at the time, he could've ordered them to fling her out of the plane and they would have!
Re: Missy's plan.
As Missy was so fond of pointing out, she's bananas. Or at least, likes to put that on. You'd think that Time Lord medicine would have cured sociopathy, but I guess not. I reckon she was trying to break the Doctor, as usual, and turn him into a willing participant. Well, that was always going to end badly for her.
Re: Missy's death.
Could go either way, honestly. The Brig did blast her with a cyber-weapon, and he'd be familiar enough with Time Lords to probably have set the thing as high as it would go. Cybermen do prefer to kill humans so they can convert them, but they have to be able to ramp up the pew-pew power, if enough cyber-blasts are capable of overloading a Dalek's shields and blasting it to bits even through its armor. One-on-one, a cyberman's not a match for a Dalek, but we've seen them acquit themselves admirably in the middle of pitched firefights where they can focus fire on individual Daleks. So, it could go either way; a full-power shot from a cyberweapon to a Time Lord might be enough to kill them dead even if they had regenerations remaining, or it might not. Even if not, however, we don't really know how many regenerations the Master had left; he'd undoubtedly spent at least five, and probably more. Missy might have been his last, or not. Or, it's entirely possible that the blue of the cyber-blast covered up Missy's blue teleporter, and she's not dead. Or she was killed and teleported out as she was in the process of dying, and Regenerated somewhere else; the Doctor did say she had to have a TARDIS somewhere else. We may or may not have seen the last of the Master/Mistress.
Also, do note that the Brigadier only fired /after/ he was certain that the Doctor was going to. It's a very minor thing to think of, but it clearly was a measure of his respect for the Doctor. He would have had every reason, every justification, and even every authority, to execute Missy unilaterally on behalf of the United Kingdom and the Planet Earth, but he respected the Doctor so much - and respected the Doctor's jurisdiction over another Time Lord so much - that he stayed his cyber-gun until he was sure that the Doctor had made the decision to fire. Then he, like the Doctor sparing Clara from having to do it, spared the Doctor from having to do it. Clearly, Brigadier Sir Alistair Gordon Lethbridge-Stewart isn't the kind of officer afraid to get his hands dirty the way Danny thinks of most officers.
Re: The Master returning as Missy.
Obviously, something happened. The last time we saw the Master, he was marching on the Time Lord Council with vengeance in his eyes, and was spending Regeneration energy to counter Rassilon's technology-granted power. Even if he prevailed and slaughtered the council without taking a mortal wound in the process or needing to regenerate, of course, Gallifrey was being pulled back into the Time War, and he was trapped on a planet besieged by Daleks. Lots of opportunity there for him to beef it and Regenerate as a guano insane Scotswoman. Or, hell, he might have triggered the Regeneration voluntarily, just to change his face. Or, for another switch altogether, he might have used simple transhuman technologies (trans-Time Lord technologies?) to give himself a full body/accent revision /without/ a Regeneration; we know that Time Lord tech is certainly advanced enough for that. Suffice to say, the Master returning as The Mistress is not something that makes me go "that can't be!"
Re: Nick Frost as Father Christmas.
I'm glad I sat there digesting the end on my couch, rather than ending the on-demand playback I just watched, or I'd have missed the stinger. Clearly, they're setting up the Christmas Special. And we all know what the Doctor's Christmases are like, so undoubtedly there's going to be much with the running and the shouting and the screaming and probably the dying. But Nick Frost as Father Christmas? Heh. I wonder if Simon Pegg is going to be joining them... I hope so. That should be a good one.