Roots: John Donne's Devotions upon Emergent Occasions, no. 17 (Meditation) aka 'No Man is an Island' ("Ask not for whom the bell tolls"). The Doctor likens the hyperspace incident to a Moebius strip.
Double Entendres: "Trying to shake me off, are you? Well it won't work!"
"What is this, the Land of the Dead?"
Continuity: Time's End is the theoretical point at which the physical forces in the Universe are depleted and distorted — a maelstrom of utter chaos caught in the moment between nowhere, no time and no space. Subsequently, beings caught within its influence but freed from natural governance have the power a of Time's End at their disposal. The creatures encountered by the Doctor here are such beings, having preyed upon the remnants of previous species originating from Earth, but doomed to be entrapped and ripped from time and space by the dominant alien creatures of Time's End once they achieved the evolutionary step that would bring them to the edge of the Solar System. As the Doctor doesn't recognise them, nor the potential billions of others also trapped, he surmises that all were similarly removed from time as well, reduced to a screaming singularity of pulverised matter.
Human space exploration owes much to the little-known (by the Doctor at least) Trevor Ridgley, a rocket scientist for the War Office who first conceived the structure of what would eventually become a Stardrive in a 'doodle' carried with him on the Stapley Moor Riverside line engine Ivy Lee, destined for Hill Langton on 7th September 1952
The Valiant is a spacecraft carrier and a significant part of Earth's frontline defence against alien raiders. Its compliment is a squadron of Damocles fighters, the deadliest fighter craft of their age, and the envy of Earth's enemies. The Exeter is the closest vessel to the Valiant. Both are fitted with cryogenic units to place personnel (and stowaways) in stasis, and conventional nuclear weapons.
The Doctor is still without his sonic screwdriver, having meant to rebuild it. For 'a while' in his past he took up train spotting as a hobby. Two months pass for the crew of the Valiant while the Doctor and Evelyn are temporarily in 1957.
Links: Doctor locks off the TARDIS' drift compensators (Three's a Crowd)
Future history: The red cross is still used as a medical symbol. Military security locks in the late 22nd century are rather susceptible to high frequency vibrations.
There is an ore station nearby, the Jupiter Moon (presumably not actually on a moon of Jupiter's, unless spacecraft travel really is that fast in 2197. On the other hand, Io is mentioned)
Untelevised adventures: The Doctor once met and Andosian privateer called Dr Leopard (melodramatic names are characteristic of Andosian leaders). He was eight feet tall, had rippling mauve muscles and three heads.
Location: The Valiant, Pluto's orbit, 16 January 2197. The Ivy Lee, 7 September 1957.
The Bottom Line: "Time's end. I have always been here. And now so will you"
A ghost story done with strict economy. The Doctor's quick elevation of assumed guise from 'Constable' to 'Detective Inspector' is a nice throw-away that, while inessential to either the Doctor or the listener, nevertheless assures us that Briggs' understanding of the character is sound indeed.