Last of the Time Lords
Roots: The central idea if this episode (the world going to pot and then time being reversed) was previously used in Millennial Rites, which got it from the X-Men stories An Age Undreamed Of and Inferno. Though the idea could have also come from Superman.
We hear the Scissor Sisters' I Can't Survive. Professor Docherty mentions Countdown, Des Lyneham, Des O'Connor, and Bill Gates. The Master mentions Gandalf from Lord of the Rings.
Goofs: The lightning strike that killed a Toclafane was said to have a charge measured in joules, which is the SI unit of energy. Charge is actually measured in coulombs.
Why does the second ageing process turn the Doctor into Dobby the House-Elf from Harry Potter?
How does the Master know about Rose Tyler absorbing the Time Vortex? [Yana overheard the Doctor and Jack talking about it in Utopia. Though it's still a weird reference for the Master to make.]
How does everybody know the exact time to start thinking about the Doctor? [Presumably Martha's sending some sort of signal via the Archangel network, though it's not clear how she knew how to do this.] Come to think of it, the whole plan is remarkably complex for the Doctor to have communicated it in such a short whisper.
Also, given that Martha's spreading her message far and wide to everybody she comes into contact with, how has there not been a single person who decided to sell her out and reveal her actual plan to the Master?
How exactly does the archangel network enable the Doctor to restore himself to youth, disintegrate his cage, and float across the ship?
If destroying the paradox machine rolls back time to after the President's death, what happened to the Toclafane who killed the President? [The effect rolls back everything outside the Valiant. So those Toclafane have simply disappeared from history, as has any human who was on the Valiant when the President was killed, but not during the reset.]
What happens to Martha's jacket? She's wearing it when she leaves the Valiant in The Sound of Drums, in commando gear when she gets back to the UK, and has it again after time resets. [She gets an identical jacket from the TARDIS wardrobe or from a shop.]
Technobabble: Opening up a rift in the Braccatolian space. Black hole converters. Tune myself into the psychic network and integrate with its matrices.
Continuity: The Master has enslaved the people of Earth. Camps include Nuclear Plant Seven in the UK and Shipyard Number One, which covers Russia from the Black Sea to the Bering Strait. In one year, they have built 200,000 warships for a war with the rest of the Universe. The Master is planning to build the new Time Lord Empire. There are statues of the Master all over the world, and he has carved himself into Mount Rushmore. London is now full of wild dogs. Medical staff have special dispensation to drive, so that they can help out at the labour camps.
The Master has Martha's family working as servants on board the Valiant, Jack kept securely chained up, and the aged Doctor kept close at hand. His laser screwdriver has isomorphic controls.
The Catriga Nova has whirlpools of gold.
The Archangel Network consists of 15 satellites and is making the people of Earth scared. Though not scared enough that there isn't a resistance movement willing to help Martha.
The Toclafane spheres can only be damaged by electricity. A lightning strike in South Africa once brought one down. Martha obtained a disc with technical readings of the event. They are future humans, regressed to a murderous kind of childhood.
Jack used to live in the Boeshane Penninsula. He was the first person from that area to be signed up for the Time Agency,and acquired the nickname the Face of Boe. He is also ageing very very slowly.
There is a burst of starfire right now over the coast of Meta Sigmafolio, and the sky looks like oil on water.
Links: Martha mentions being in space (numerous stories) and meeting Shakespeare (The Shakespeare Code). There's a flashback to Smith and Jones. The Master mentions Sea Devils (TheSea Devils) and Axons (The Claws of Axos). The Doctor also recalls his and the Master's encounters with the Axons and the Daleks (Frontier in Space).
The Toclafane turn out to be the humans from Utopia.. The master mentions the Doctor having companions who could absorb the Time Vortex (tv]The Parting of the Ways[/tv].
Extras: This episode had an episode of Doctor Who Confidential.
Location: England and the Valiant, 365 days after The Sound of Drums. The Valiant, Wales, and London on the same day as The Sound of Drums.
Future History: The Toclafane turn out to be the people from Utopia.
Unrecorded Adventures: Martha spends one year travelling the Earth. She says that she's been to the ruins of New York, the fusion mills of China, and across the radiation pits of Europe. She claims to have collected pieces of a weapon in San Diego, Beijing, and Budapest, so has probably visited those particular places. Rumours say that she sailed the Atlantic, walked across America, and that she was the only person to get out of Japan alive. Details of some of these events would later be reveal in the book The Story of Martha.
The Master claims that the Doctor battled Sea Devils and Axons during the Time War and mentions that the Doctor sealed the rift at the Medusa Cascade overnight. He made the Jones family watch the islands of Japan burning.
The Master took Lucy Saxon to Utopia. She decided there was no point to anything as she saw everything dying.
The Bottom Line: 'Time was, every single one of these people knew your name.' A perfectly functional end to the story arc. The plot makes very little sense, and Simm's Master is fairly unmemorable, but there's nothing actually bad about this episode.