Trivia: At the undertaker's, the Doctor remarks on the strange behaviour of the gas light and Charles Dickens says "What the Shakespeare is going on?" This is a joke on Dickens' name, the expression "What the dickens...?" being a euphemism for "What the devil...?", making out that the phrase wasn't in use in Dickens' time and came from his name. In fact, "What the dickens...?" is much older than Dickens himself and has been in use since the sixteenth century, according to the Oxford English Dictionary.
Trivia: When the Doctor sends the banknotes flying out into the street, all of the notes have David Tennant's or Phil Collinson's (the producer) faces on them, with quotes from the Fourth and Tenth Doctor (like "no second chances - I'm that sort of a man"). The notes have since become collector's items, selling often for about 50 pounds each.
Trivia: When Harriet Jones is explaining the sub-wave network to the Doctor's companions she says "It was created by the Mr. Copper Foundation." This is a reference to Mr. Copper from "Voyage of the Damned", who stayed to live on Earth and who probably would have had the advanced technology from the planet Stow where he came from.
Trivia: The 2018 novelization, also written by Steven Moffat, includes a scene that he had wanted to include in the episode proper but couldn't due to rights issues, where UNIT head Kate Lethbridge-Stewart, while showing Clara around the Black Archive, shows her the posters of 1960s movies Dr. Who and the Daleks and Daleks Invasion Earth 2150 AD, which were loose adaptations of the first two Dalek serials, "The Daleks" and "The Dalek Invasion of Earth" starring Peter Cushing, and confirming them as existing in the Doctor Who universe. Kate then explains that the movies were made with the Doctor's knowledge, and that he was good friends with Cushing and loaned him a waistcoat to wear in the second movie. The novelization then goes on to add that the Doctor got in some trouble with UNIT for bringing Cushing to the future, to appear in a movie made long after his death - a nod to the late actor's controversial CGI resurrection in the Star Wars spinoff movie Rogue One.
Trivia: The 2018 novelization, also written by Russell T Davies, expands the scene where conspiracy theorist Clive shows Rose pictures of the Doctor in multiple time periods. In the episode, he only shows her pictures of Nine, but in the book, he has pictures of every incarnation of the Doctor up to Thirteen, as well as pictures of two incarnations from even further in the future. The two potential future incarnations are described as a "tall, bald black woman wielding a flaming sword" and a "girl or boy in a high-tech wheelchair accompanied by what appeared to be a robot dog". Conveniently, Rose happens to turn away just as Clive shows a picture of the Tenth Doctor, since she can't see him before the regeneration in "The Parting of the Ways". On a final, amusing note, the picture of Thirteen shows her being chased by a giant frog outside Buckingham Palace.
Trivia: There is a scene where several of the robot spiders are scrambling through ducts, and one of them bumps into the camera, despite the robots being CGI. This is a reference to a legendary blooper in the First Doctor serial "The Web Planet", where one of the Zarbi - large, ant-like aliens - bumped into the camera.
Trivia: The Clockwork Droids that serve as the episode's villains came from the SS Marie Antoinette, a sister ship to the SS Madame de Pompadour from "The Girl in the Fireplace". It's not surprising that the Doctor finds the situation familiar. The fact that he doesn't recognize the name of the ship is also unsurprising - he never found out what the Madame de Pompadour was actually called in the previous episode.
Trivia: When Clara jumps into the Doctor's timeline and is shown encountering the Doctor - usually indirectly - in various incarnations and adventures from the classic series, the adventures chosen were mostly ones regarded as being badly written and/or having nonsensical plot elements, with the implication that in-universe, those plot elements were due to the Great Intelligence's meddling. Examples include the notorious instance of the Seventh Doctor dangling himself from a cliff for no reason from the serial "Dragonfire."