Roots: Classical myth: the name Eumachus, the Ruhk is likely based on the Rokh or Roc of Persian myth, the Doctor exploring the reconfigured TARDIS aided by a ball of string recalls Theseus in the Labyrinth, Gammades mentions sirens (The Odyssey), an Oracle and a Sphinx; The sack of Shimanzi recalls the siege of Troy. Phyton may be a deliberate anagram of Typhon, The crew are surprised to see Lady Vuyoki walking straight through the creatures like Moses parting the Red Sea. The Rime of the Ancient Mariner and The Flying Dutchman. Brewster mentions his mother's favourite penny dreadful, The String of Pearls: a romance (aka Sweeny Todd.)
Fluffs: In scene two the airborne Eumachus seems to say "I'm like a chitinous string!"
Goofs: Brewster seems to know a lot about his mother despite having only remembered her funeral.
Dialogue Triumphs: Brewster and Lady Vukoyi: "Didn't think I'd desert you, didja? I'm the bad farthing, always turning up" "-But it takes such a long time from one 'always' to the next."
The Doctor in a piece of TARDIS circuitry: "Outside its home it's about as system-compatible as a biscuit in a waterfall"
"I am pinned between the beating wings of a prophecy and a curse. And they will tear me apart!"
Continuity: The Reef is a small, barren, inhospitable rock made of fast-growing space coral - the Doctor says that one grain of it on a spacecraft's hull would be enough to trap it - contained within a bubble of existence where nothing can exist. Its perimeter may be traversed by going in a straight line. The Doctor describes the sensation of being on the Reef as akin to being underwater - the energetic patterns of the Time Vortex play across the surface of the bubble above them, though no sun or stars can be seen.
The Ruhk says it comes from' an eternal everness' beyond the passages to time. These are pan-dimensional places the Doctor says he'll probably never go to - its feet would usually never touch the ground, and indeed the dimensions here bind and crush it; the Doctor says in 'our' heavy dimensions it would "crumple like an umbrella in a gale." The true pan-dimensional form of the Ruhk is more beautiful to behold.
The Doctor recognises the Gamma as a coal-stoked Calimeran galley, one of the classical pioneers of temporal travel. Gammades tells the Doctor that when he was newborn he was taken to an Oracle who foretold his death in glorious battle. His first ever toy was a sword and all through his schooling he was told he was going to be a hero. During the sack of Shimanzi in the Wineskin Cloud Captain Gammades slew the "blood-popped Hippodile of Yoth" in hand-to-tooth combat". At the burning of the Sable Empire, a wounded Sphinx came prowling through the field of dead, found him where he lay bleeding and cursed him to eternal life.
Lady Vukoyi rules Maribu, a world and late dynasty known to the Doctor, although he explains that it rules at the other end of time to Gammades. On Maribu each year, at the dead of harvest, a tribute flies in thanks to Maribu, their Sun. Lady Vukoyi was chosen to be his bride, and packed away in her bridal urn on a ceremonial starship with 50 jars of grain. After a disastrous storm and she crashed on the reef, apparently dead and waiting here ever since for the messenger of the all-knowing spirit Old Birth, to lead her from the 'afterdeath' to her next life. Preparation for being led to the afterlife seems to involve meditation upon one's past sins. The Doctor translates the hieroglyphs on Vuyoki's bridal jar roughly as "Maribu, Great Star, take into your fiery heart this lost soul by whose murderous hand 2,000 slaves met their deaths. Cleanser of the wickedness for which we on this world have no remedy". Lady Vuyoki's slaves are fed mud "so they know their place"; she refers to her mockers as "giggling hyaenas"
Among the equipment rendered missing by Brewster's meddling with the TARDIS is a food machine, fault locator, the conceptual geometer (The ship is effectively dead without this) and the power lens unit. The Doctor says equipment wasn't designed to be compatible outside the TARDIS. When the Doctor opens the door of the TARDIS and lets the Commander see inside, it is dark and void-like because it has no dimensional structure.
Links: The TARDIS fault locator is missing (Inside the Spaceship), as is the food machine (The Daleks) and conceptual geometer (The Horns of Nimon)
The Bottom Line: "The beacon. It sings this place alive. It sings away the dark"
More magical realism from Platt, but a strange mish-mash of the melodramatic (Vukoyi), the bombastic (Gammades) and the epic (the Rukh), not to mention the mundane and vexing Brewster, who is turning out to be a most frustrating foil for an all-too forgiving Doctor.