Fridge / Doctor Who S34 E1 "Deep Breath"

• The Doctor characterizes whoever placed the "Impossible Girl" ad as "an egomaniac, needy game-player". We later learn the ad was placed by Missy, previously known as the Master — someone of whom "egomaniac, needy game-player" is an absolutely dead-on description.
• The Doctor redecorates the TARDIS with bookshelves full of books and some blackboards, probably hoping to make an English teacher like Clara feel more at home.
• A passing reference in this episode reveals that the spaceship Marie Antoinette, and its sister ship Madame de Pompadour, date from the 51st century. That seemingly-trivial detail actually makes both sets of Clockwork Droids - the ones from "Deep Breath" and the ones from "The Girl in the Fireplace" - products of the same era that produced Mr. Sin, the Peking Homunculous from "The Talons of Weng-Chiang"! So it's not actually that weird that the Droids would take to using organic body parts as substitute components: Mr. Sin had a pig's brain for an operating system, proving such machine/organ interconnections aren't a novel idea in the century they're from.
• In the previous Clockwork Droids episode, it was the clicking of their gears that gave them away. This time, it's the sound of breathing that gives Clara away. Either way, it's the basic mechanics of the hidden party's internal parts that betrays their nature.
• The fact that Missy welcomed the Faceless Man to the Promised Land makes perfect sense: he's essentially a prototype for the type of upgrading she has planned for humanity's dead. Not only that, but it also makes sense that she'd direct the Doctor and Clara to Mancini's, of all possible places for a rendezvous: she knows the Doctor will shut the Clockwork Droids down, thus eliminating the competition for human remains.
• When Clara's legs aren't long enough to reach the sonic screwdriver, the Doctor makes a comment in passing that he misses Amy, which looks like just a funny little Continuity Nod. It's actually a clever bit of Fridge Brilliance for two reasons: first, because as he was regenerating into Twelve in "The Time of the Doctor", Eleven had had a vision of Amy bidding him goodbye and therefore she would not have been too far from Twelve's mind - in fact, Eleven's attachment to Amy may actually be why Twelve ended up regenerating with a Scottish accent in the first place; and second, it works on a meta level referencing the mystery of why Twelve has the same face as the man he saved in Pompeii, since Amy's actress, Karen Gillan, also appeared in that episode.
• Vastra's comment about "here we go again" seems a bit odd, given that she's never seen a regeneration before. However, it can be interpreted in a more general sense: She's taken care of the Doctor before, in "The Snowmen," and can tell that she'll have to do so again.
• The episode's title is "Deep Breath". Coming immediately after the cataclysmic events of "The Name of the Doctor", "The Day of the Doctor" and "The Time of the Doctor", its relatively non-epic storyline offered audiences their first chance to catch their breath in some time.