Roots: Cluedo ("It was the Professor, with the spanner, in the Power Room!") Mark Twain ("Rumours of my death, et cetera")
Goofs: Somewhere during their conversation Tamsin and the Doctor discuss burial regalia, which later becomes "battle regalia".
Dialogue Triumphs: "Move any closer and you're baked Alaska!"
Professor Schooner's constant misunderstanding of the Martian language is a hoot, even on his imminent death: "Oh. Still, I got it half right."
Double Entendres: "This isn't Phobos you know"
Continuity: Martian city base is on Olympus Mons, home to three hundred thousand people. The base has a fission chamber
The main projection dome is the largest structure on Deimos, housing the ioniser, a vital component in the Mars Terraforming programme which was abandoned due to the galactic recession (which continues to this day) and some technical obstacles. Earlier plans for a series of artificial suns to heat the planet (see: Links) never got off the drawing board. If it had gone ahead, the ionising project would have re-ionised the Martian atmosphere, with the next step being the satellite suns for warming the atmosphere.
Professor Boston Schooner is the foremost expert on Martian culture (that said, he's not that good), and curator of the museum on Deimos. Contemporary technology includes Hologram cameras and Wi Fi induction loops for hearing aids. Power cells for the shuttle are based on decay emissions, transmitted via microwave.
Lord Vasslor was the architect of the Tombs, although Izdaal allegedly ordained them made. His tomb features geometric art typical of the Fifth Dynasty. In the reliquary is the statute of a Lord Valexx "slayer of the weak." The Ice Lords are buried in full regalia, though it is unclear whether this is burial or battle regalia during the Doctor's and Tamsin's conversation. It is not of the Second Dynasty.
The core temperature of an Ice Warrior is minus twenty degrees Celsius. They are identified here by the Doctor as indigenous to Mars. Those Warriors hibernating in the asteroid belt will awaken "in a few centuries", according to the Doctor
Tamsin took ballet lessons. For one summer she worked at the London Dungeon as a 'drab' re-enacting the crimes of Jack the Ripper.
Location: Below the crust of Deimos, possibly April, 23rd century. The events of the Seeds of Death are referred to here as having taken pace "centuries ago".
Future History: The terraforming of Mars would have involved a series of artificial suns (see: Links) set in orbit around the planet, but was brought to a premature end by a global recession (to which, in part, the cost of the project contributed.)
Untelevised Adventures: Did Tamsin and the Doctor spend a fortnight in Provence?
The Bottom Line: "There is no honour in allowing the defenceless to survive!"
More of a set-up piece than a complete story by design and structure - this just as 'part one' written all over it. Nicky Jensen is wasted, but the nastiness that gathers over the episode points to something bigger waiting in the wings. We hope.