Madame Vastra's line "Well then, here we go again" made me chuckle - recycled from the Brigadier in Planet of the Spiders. It seemed fair enough that a post-regeneration story should be a bit wobbly from the Doctor's perspective; perhaps less so in this case from Clara's, although her whole time-line is obviously jumbled, to say the least. Indeed, perhaps up to the point in the restaurant where they both realise that neither of them placed the newspaper ad, the relationship in this episode has been rather reminiscent of that between Colin Baker and Peri. The scene where the Doctor wonders why he "chose" this face is interesting; I've seen some comments that seem to interpret that literally, whereas I'm reminded more of Davison's "you never quite know what you're going to get". If it's a choice, it's subconscious. It's an interesting symmetry that Caecilius ends The Fires of Pompeii with a shrine representing the TARDIS, whereas the TARDIS now has, in some sense, a reproduction of Caecilius. The "Scottishness" is obviously quite topical and did have some laughs ("I'm allowed to complain!") but I don't know whether that will necessarily resonate internationally, or over time.
In principle, I was very pleased to see a return for the clockwork robots - it's a toss-up between The Girl in the Fireplace and School Reunion (more, peripherally related to that, later) for my favourite new-Who story. I'm not sure they were quite so successful this time around; though I suppose it's fair enough that they would exhibit the same basic problem as their colleagues.
The weakest part of the story was probably Matt Smith's telephone call, but I can live with it. It was fun to hear the Doctor had planned to take Clara "home" but had landed in Glasgow - not only because it retains a number of Police Boxes, but also because we both thought of Tom Baker leaving Sarah Jane Smith in Aberdeen. I'd like to think references like this were conscious rather than haphazard, though obviously after 50 years it must be difficult not to repeat yourself from time to time.
Most of Teh Interweb seems to think Missy is the new Master, so they're probably right, although I'm never that enthusiastic on that score. I rather like strange_complex's alternative ideas, particularly that she might be a regeneration of River Song. To my mind, the final scenes of "Paradise" did share the same slightly-soft-focus look with the ending of Silence in the Library/Forest of the Dead.