Roots: The background story concerns (for want of a better description) a 'war in heaven' - the Elohim and Cherubim are orders of angels referenced in the Bible (Exodus) and Torah; while Michael and Gabriel are of course Archangels. The Doctor sings from Gilbert & Sullivan's 'Nightmare Song' (appropriately from Iolanthe or The Peri and the Peer) and quotes from Macbeth ("lay on, Macduff"). He quotes from Hesiod's Works and Days ("moderation is best in all things") Jack Be Nimble. The music onboard Paradise 5 includes The Dance of the Sugar Plum Fairy (whistled by Mr Winterbourne) and The Blue Danube Waltz. Michael paraphrases Rhett Butler from Gone With the Wind ("frankly, dear heart, I don't give a damn"). Part of the Doctor's distraction in the paradise machine includes Oranges and Lemons. The Righteous Brothers (the Doctor's sonic lance "hums a little Unchaining Melody"). Mr Winterbourne quotes the chorus to 'Monster' by The Automatic.
Technobabble: A side-effect of the Elohim's presence is Exothermic osmotic energy transference, i.e. getting cold (the Doctor is showing off, as Peri points out)
Goofs: "Give the Daleks some credit, at least they fight their own wars and don't rope in someone else to fight them for them" (apart from Ogrons, humans and the like, that's pretty spot on)
Slightly unfair as this story was produced by a different company well before the latter: the Doctor claims to have not visited Manhattan since 1965, but was there in his Fourth incarnation in 1976 (Demon Quest: Starfall)
Fluffs: Colin Baker's delivery of "It doesn't matter how strong your will is" - possibly a tribute to Anthony Ainley's Sir Gilles Estram?
Double Entendres: Peri seems to say "What are the doodies of Paradise Five staff?" (snicker)
"Well done for finding my hidey-hole" "-I just followed the humming"
Dialogue Triumphs: "You're both criminals" "-We're in the leisure industry, of course we're criminals"
"That's the Doctor's distraction" "How do you know?" "-Because it's loud and striking, just like him!"
Continuity: The Targos System has at least four planets (mention is made of Targos Epsilon as a business destination). Most of the hotels on Targos Delta are automated. Targos Beta has lava oceans on its surface. Paradise Five is a leisure space station orbiting it. An exclusive resort, entry is by invitation only. Its aquariums host species of marine life (including the angel shark) from over a hundred oceans on fifty odd planets, according to the Doctor.
The Elohim are insubstantial (someone thinks they could "simply float through walls like smoke) and clothed in decaying robes. They are fighting a war on another dimension.
Peri was a straight A student at her college, coming top in her year in Botany. She always wanted to travel the Amazon and have a plant named after her. Each Thanksgiving her family would go to New York City. She has a lot of experience with waitressing in cafes.
The Doctor has with him a sonic lance, which appears to work to a similar end as the sonic screwdriver. He says he hasn't been to Manhattan since 1965 (see Goofs and Links). In his pockets he carries some smelling salts he took from Pliny.
Untelevised Adventures: The Doctor claims he learned the art of slapstick in Hollywood whilst being "the fourth Stooge" as part of The Three Stooges.
Links: Peri recalls the vents of The Hollows of Time. The Two Doctors (Gumblejacks) The Deadly Assassin (The Doctor mentions the Matrix), The Ribos Operation (jethryk) The Doctor's comment "I can move like a cat if the mood takes me" is repeated in Andy Lane's Seventh Doctor story A Thousand Tiny Wings. The Doctor was in Manhattan in 1965 during The Chase, likely the date he is remembering (but see also: Goofs). Mention is made of the Psychic Circus (The Greatest Show in the Galaxy).
Location: Paradise 5 in the Targos System, the 35th Century.
The Bottom Line: "So this is Paradise. Not quite what I expected"
An Epicurean Doctor and a Peri with brains and a gold bikini - all boxes ticked. With a documented history that would have placed 'Old Sixie' with Mel as the companion, this version of Paradise 5 is a squint-and-don't-overthink-it affair, but it deserves more attention than this companion swap might give it. Andy Lane's contribution is a worthy episode in itself, and the sinister inclusion of the Elohim tied with the (necessary) mid-Eighties aesthetic means the result is a cut above the average, and much more than a patch-job. A good story, in other words, with its regulars in fine form.