Roots: Goodman admits that part of his teachings are based on the parable of Robert the Bruce. Star Trek (Karen refers to 'beaming down' Lucie)
Goofs: If Lucie is so vital to the plan (viz tracking her with the stellar manipulator) why didn't the Headhunter just track her down herself (as she did at the end of The Vengeance of Morbius)? [It pads out an episode and shows us inside the organisation. Perhaps the Headhunter doesn't trust Karen to such an extent that she'd rather leave the entire plan to coincidence].
Fluffs: "A kind of yin and yan thing"
Technobabble: Psychic pulses travel at a hundred and fifty times the speed of light.
Dialogue Triumphs: "Another thing that turns people weird is having their minds taken over by intelligent mutant spiders" "...please tell me that was just a non-sequitur."
"What should we do if they just kill us, on the spot?"
"-I should imagine we won't do anything"
Continuity: The stellar manipulator can manipulate any form of solar energy from any kind of sun [presumably including novae as applied by Omega]; in doing so it drains the energy of the respective sun and stores it. Whilst in Earth's orbit its ambient light is bright enough to blot out that of the stars, even when it is on the other side of the planet. It has isomorphic controls (which are "hellishly difficult to break', although the Doctor implies he has past experience in doing so) and is programmed in Gallifreyan computer language.
The Metebelis spiders can move on the astral plane, but require a host to travel 'to.' As the 'spider heaven' the manipulator also contains the living consciousnesses of alien species.
Metebelis Crystals concentrate and amplify thought - even to the extent of curing mental illness. Their counterparts, dull, shapeless stones from the same planet, act as effective counteragents to the crystals' negative effects. The Doctor having previously discovered this, kept a few in the TARDIS as they were useful.
The TARDIS' systems are more than enough to contain a living consciousness. As a consciousness inside that TARDIS, Lucie is privy to its 'thoughts' about the Doctor.
The bomb sent to the Doctor has fragments of Polonium 210 in it (all isotopes of Polonium are radioactive). It has the effect of knocking the Doctor out for twenty-three days as he shuts down his respiratory system and puts himself into a coma to beat the poison.
The Headhunter has apparently programmed Morbius' stellar manipulator to track and follow Lucie after having secreted some of her DNA away. It is inferred that she somehow palmed it after the Doctor apparently threw it into the Great Ocean of Orbis and has been with the Eightfold Truth for the past two years. She has used many aliases and identities, to the effect that she may have forgotten her own true name.
Karen, it may be inferred, is rather short and not particularly attractive. While in nthe servce of the Headhunter the two of them planted the Metebelis crystals in the Yorkshire caves to be found by Goodman.
The Doctor admits that he is actually quite fond of spiders. Hand to hand combat isn't his forte.
Future History: The pound is still in circulation in Great Britain, as is Newsnight.
Links: This story continues that of The Eightfold Truth. Planet of the Spiders. Orbis. Lucie identifies a Trel in the Great One's virtual space (Sisters of the Flame), which the Doctor earlier compares to the Matrix on Gallifrey.
The Bottom Line: "Please tell me giant mutant spiders aren't behind all this"
The final end for the Headhunter? Katarina Olsen's too-fun nemesis fades into oblivion, her final triumph being that the Doctor never knows her name. Eddie Robson's control over the two-parter is still a thing to be admired, even if Lucie's backup on the TARDIS mainframe ash the distinctive bouquet of a Deus Ex Machina. With the stellar manipulator, Lucie's involvement with the league of nature and the Headhunter and Karen all having their boxes ticked off and packed away, the Doctor and Lucie appear to have had their bumpiest ride come to a gentle and life-affirming end. Roll on the Christmas special...