Roots: This Island Earth (the Interociter, which the Doctor implies, is inspired by the movie), meme theory. 'Global Warning's laser defence system recalls the Reagan-era Star Wars programme. The Doctor likens Nyssa to Joan of Arc and the TARDIS as Noah's ark. Three Blind Mice.
Dialogue Triumphs: Alice: "Are you guys CIA?" The Doctor: "Pending a fuller explanation, hold that thought"
'Zero room? On the account of how much furniture they have in it?'
'By just standing here and doing nothing...I have defeated you!'
Double Entendres: "Don't get excited, Alice, we're part of The Dalek Invasion of Earth."
Technobabble: A wormhole is a traversable topological anomaly in space-time connects Rhodes in 1320 to wherever they are now
The TARDIS toolkit includes an Electron Probe.
Time-suspended actinide metal allows the energy of its radioactive decay to be safely can be used as a means of power.
Continuity: In the alternative 22nd Century Earth Global Warning is an early warning system using time technology (years ahead of what the Doctor knows to be correct) and incorporating a massive laser system powered by fifty gigawatts of energy per device. Its head General Tillington knows of the Doctor and has followed his progress, waiting for his arrival in order to beat back a projected Dalek invasion. His team employ a "pre-construction" created by their TLTs (Time-Line Technicians), trained 'intuitives', or time-sensitives, who interpret future events in a Shaping Chamber and transform them into 3-D images; the closer these images correspond to the current timeline the clearer they appear. Skyscooters are compact, two-person vehicles that can fly and can take off backwards.
As they lack a protection protocol (see below), every time Dalek time journeys overlap, an intersection is created by the convergence of time tracks, causing a potential anomaly. After repeated attempts to occupy Earth in the 22nd century the combined and converging time tracks have allowed a notion of 'Dalek-ness' to permeate through time, fed by the Daleks transmitting energy across space and time, using voices to encourage conditions on Earth, making humanity susceptible to Dalek concepts and inspiring the creation of model Dalek toys from actinide metal, a vessel for miniature Dalek mutants - 'nano-Daleks.'
The Pan-Temporal Ambience is a world created by the Greylish, a partly-organic individual perfected over generations of Dalek breeding and from whose tissue all nano-Daleks have been created. Finally brought into being and sustained by a Dalek group mind-share, the Greylish's own mindpower sustains the Ambience, which houses a city composed of towers of full-sized Daleks stacked like bonded molecules. From this 'North Pole of time' where all the time tracks meet and alternative realities intertwine' a vantage point from where the whole chronology of war's folly can be seen.
The TARDIS has recently created a new Zero Room (see: Links.) A red light on the TARDIS console indicates the reception of an Interocitor's transmission. The Time Track Crossing Protection Protocol is a pre-set circuit found on all TARDISes and is located under the console. Its function is to prevent the occupants from returning to the exact time and space coordinates as a previous visit - the recursive consequences can be dangerously unpredictable. It is supposed to be constantly engaged, but the Doctor hasn't examined the TARDIS' one in 'years', and it has become quite unreliable, working rarely if at all.
The Doctor, inspired by a sci-fi movie (see: Roots), has created an Interociter, a communication device which works on actinoidal energy and allows communication across different temporal areas. For possibly the first time in the [audio and television] series the Doctor is strip searched.
Links: The Dalek Invasion of Earth, The Mutant Phase, The Space Museum (time tracks), The Krotons (The TARDIS' HADS). The Doctor recalls the city of Logopolis (Logopolis). Resurrection of the Daleks (Dalek time corridors). The Doctor's Interociter returns in Lucie Miller, which takes place during the actual Dalek Invasion of 2157.
Future History: Unaware that he is in an alternative timeline the Doctor claims that by 2158 Earth should not yet have access to time technology.
Location: The Savoy, London: 2158, Rhodes 1320, Petersberg (Virginia), 30 July 1864, Vietnam during the Vietnam War (somewhere between 1962 and 1971 judging by the use of Agent Orange).
The Bottom Line: "The mystery of the invasion that vanished..."
Problematic. And not entirely logical or satisfying. Salvaged from an overlong script (hence the 'adapted by' credit) the story is a mishmash of mad schemes and wilfully eclectic characters. Of the pseudo-companions ranging from pleasant but bland (Mulberry) to jarringly annoying (Alice), newly 'freed' slave Floyd is probably the best of the three for discovering his new freedom in a practical way without this being a plot point at the same time. With such an epic cope and bizarre cast the result is some way towards Moffat-Era Who, in spite of the efforts of all involved.