Roots: The title comes from the 1742 poem "Night Thoughts" by (an unrelated) Edward Young. Ace quotes bugs Bunny ("Ehhh, what's up, Doc?") and Yogi Bear ("Smarter than the average bear"), and calls the Doctor 'Batman'. Hex paraphrases Old Mother Hubbard. "Oranges and Lemons" Goldilocks and the Three Bears ("someone's been in my mobility chair" "and someone's eaten my porridge"). The Doctor quotes from Mary Howitt's The Spider and The Fly ("Will you walk into my parlour?..."). Gravonax Island likely takes its name and inspiration from Gruinard Island, aka 'Anthrax Island', the site of experiments of weapons-grade anthrax, finally decontaminated late in the 20th century.
Dialogue Triumphs: "The human race seems to have perfected everything, except itself."
Continuity: The island is in the Outer Hebrides, and while it has running water and an intermittent power supply there is no permanent population there, with other islands only contactable by radio and boat. Sibley Hall is over ten years old (and is probably much older still) and there is a chapel nearby. During the Great War, the dozen or so inhabitants of the island were relocated while the site was used for experiments with gas weapons, including Gravonax Gas, the deadliest of gases to be used in warfare. Everything on the island withered and died - trees, fish and wild animals in particular, which suffered a long and lingering death. Years later, the island was cleaned up, but no-one returned to live there. Gravonax poisoning has no cure - the first sign of infection is blindness, followed by slow suffocation. After time the victim's eyes burst out of their orbits - the Doctor says its symptoms are some of the most readily-recognisable to man (or it would be to the Major).
The celebrated scientific theorist JJ Bartholemew's work on the transmission of sub-atomic particles is regarded as a foundation for the eventual unravelling of the secret to time travel on Earth. Despite this, her 'Bartholemew Transmitter', a device capable of relaying a sub-atomic particle (or, in this instance, a particle connected to a message) back through time to a remote receiver, becomes little more than a party trick, as its effects are too slight to influence the Web of Time. The result of the process merely enables participants to experience a ghostly and short-lived taste of what might have been, like a double exposure on a photograph.
Hex was raised by his grandmother and until the age of six believed her to be his real mother - he doesn't know who his real father is (see: Links). He has seen the effects of suicide by ingested sulphuric acid before, once while working a night shift.
Ace introduces herself as 'Ace McShane', and thereafter "just Ace". She remembers her mum crying for days when her grandmother Kathleen died; though she was only three the memory burned itself into her mind. She had an imaginary friend as a child. Her first pet was called Marmaduke, and the first street where she lived as a child was Beech Road.
The Doctor says his field is 'macrocosmology' (although he really just dabbles). He is familiar with the works of JJ Bartholemew, having read her thesis.
Links: Hex's grandmother is also mentioned in Live 34 (it is likely therefore that his story about his father in that adventure is fabricated, or comes from elsewhere), while Ace met her grandmother Kathleen Dudman and infant mother in The Curse of Fenric.
Location: Sibley Hall, on Gravonax Island in the Outer Hebrides, date unspecified (presumably no more than ten to twenty years after the Falklands War), winter.
The Bottom Line: "They can be terrible things, night thoughts"