Roots: The Tragical History of Doctor Faustus (from which also originated the epithet 'the face that launched a thousand ship', used by the Doctor regarding Peri in episode two), Marlowe's Tamburlaine is referenced several times. Aztec mythology (the legend of Quetzalcoatl). Peri's Elizabeth II imitation parodies HRH's frequently-used greeting during royal tours and visits (apparently).
Intertextuality: Platt's expansion of Clegg's script offers several nods to his thematically-similar, earlier Unbound sequel A Storm of Angels, including mention of John Dee and his Aztec-crafted obsidian 'shewstone', Sir Francis Walsingham, and Elizabeth I prefiguring the public patter of her Twentieth Century namesake: 'And what do you do?"
Goof: The Doctor and Peri discuss Elizabethan England being the earliest part of history she's visited, which rather overlooks The Eye of the Scorpion, The Church and the Crown, and Son of the Dragon to name some stories.
Double Entendres: "Here sir, want to try my hot codlings?"
"Your tradesman's door stands open, hostess"
"Back door, front door - 'tis all the same"
Continuity: The Omnim were an insubstantial race of intelligent creatures who lived on a world of combined colour and harmonics. Being able to create vibration at will, their global resonances grew so strong and so far beyond their control that their world shattered and was spread throughout the cosmos. As well as the solid rogue asteroid encountered by the Doctor's TARDIS, a fragment of the shattered planet found its way to earth during the time of the Aztecs, where it was carved into a ceremonial stone dagger with its hilt in the likeness of the god Quetzalcoatl. After a time the dagger was broken in two: the English privateer Cormorant claimed the dagger blade from the ailing Spanish ship Santa Isobella (whose crew were grateful to be rid of it) off the Azores after their return from the New World. En route to England the crew of the Cormorant similarly thought they were cursed, with the blade attracting the attention and cries of whales during their journey. Velez found the hilt in Madrid and through its influence has endured past the point of death under its service, sustained by the blade's energies. Weakened by the event, the Omnim now exist only as the sound of buzzing flies, and are still vulnerable to resonant vibration.
Velez's obsidian mirror has its own energy field and acts as a portal to the astral plane. Its stone matrix recognises the vibration of specific sounds (i.e. words) and creates an opening in response. The command to do so for Velez's mirror is progredior ad lucem siderum - 'onward to heaven's light'.
The Doctor has always wanted to hear Marlowe's Tamberlayne. He can work an astrolabe (of course). At the beginning of the story he is collecting data ("only two more to complete the set") on rogue asteroids from the Catalogue of Hazardous Cosmic Anomalies - the Omnim planetary body is classified 'Delta 359XQ2'
Q.v. 'Science and Magic'
Untelevised Adventures: The Doctor is familiar with royal astrologer Dr John Dee, to the point of his knowing about his obsidian mirror - have the two met? He has met Heinrich Cornelius Agrippa.
Links: The Aztecs, The Visitation (Peri mentions the Great Fire of London and the Doctor dutifully squirms)
Q.v.: The Astral Plane, Ghosts and Apparitions
Location: London, the summer of 1590
The Bottom Line: 'The past is a dangerous place, Kit Marlowe'
Better than its reputation, and perhaps much improved by Platt's presence. There's some rather lovely characterisation of the Doctor here - audibly disappointed that he missed out on a particularly garish costume hat, and his being obviously moved by Marlowe referring to him in Faustus is a nice touch. As usual, the soundscape is impeccable.
THE ASTRAL PLANE
In Point of Entry the Doctor claims that the astral plane is a mass illusion, but the plane itself is in fact a separate dimension of etheric mental energy mirroring our own. Great willpower is required to escape it, although it seemingly is still connected to our world in a physical (those on the plane describe themselves as floating above the Earth) or sensorial manner (Peri and the Doctor can smell the room burning around them.) It is, by definition and impression, an outer-worldly experience: "Like getting lost in all the world's dreams after the biggest toasted cheese supper ever."
The implication here is that astral travel and indeed connection to the astral plane, is a psychic ability. Following this conclusion we might also conclude that the ability is available to select humans with sufficient (though not always extraterrestrial) assistance, and is latent in some species who also employ psychic stratagems (e.g. the Spillagers of Winter for the Adept and the Eight Legs of Metebelis 3, as seen in The Eight Truths and Worldwide Web.) Astral projection, the ability to transport one's self across vast distances of time and space using mental power and (presumably) the astral plane, is a talent that some fans have assumed inherent in such godlike and psychically potent beings as the Fendahl and the Osirans, and perhaps lesser beings such as the so-called 'Death Wraiths' of The Haunting of Thomas Brewster. In the latter instance we might conclude that this feat requires tremendous reserves of energy, and its status as the ability of a relatively small number of almost omnipotent beings may therefore account for its rare quality.