Roots: The Shining (book and movie), The Prime of Miss Jean Brody (Scottish headmistress), Ghostbusters, Forbidden Planet (the Doctor's theory that the poltergeist is an amplified 'Id' monster), Miss Tremayne quotes from Psalms 23, Exodus 22:18, paraphrases William Cowper ('the Lord works in mysterious ways') and [possibly] Cleopatra ('I have taken an adder unto my bosom'). The Doctor says 'You'll end up cutting your throat on Occam's Razor' and name-checks William Blake and Walt Whitman.
Technobabble: The Doctor's 'ghost-hunting' equipment is attuned to detect 'interactive vibration', and includes a 'psi energy scanner'. He is able to track Nyssa down via her 'biomorphic essence' and an 'energy profile' built by him in the TARDIS (Nyssa doesn't believe him either).
Double Entendres: 'We're wondering if you've ever had any... unusual experiences?'
'Don't touch his things Alison'
'Peril and I were just trying to get it to work' (though Peril freely takes this as a double entendre)
'I'm afraid once Peril gets the bit between her teeth...'
Dialogue Disasters: 'You may find yourself a convert, and very soon if I'm not alone in smelling something'
Some glaring exposition: 'It was the big mirror on the Refectory wall...'
Continuity: Tremayne Academy is 'an outrageously expensive' finishing school in the Swiss Alps. The TARDIS 'hums' and 'feels alive' to Alison (this may be due to her telepathy). According to the Doctor, the analogy of Space as a mouldy apple is 'not entirely inaccurate'. He says to Alison 'brave heart'. Nyssa says teleportation is 'stomach churning' without the cushioning effects of the TARDIS. Despite his assertion in 'Doctor Who', the Doctor is credulous when confronted with a real 'ghost' (but explains him away as a latent, if sentient, energy mass). When he is delayed in trying to deliver the girls to their homes in time for Christmas day, the Doctor promises Boxing Day instead.
Alison is a natural telepath and Peril a telekinetic, both attributes being hereditary genetic abilities [presumably] carried down the female line. Such talents are required by the Spillagers to create a 'psychic daisy-chain' or 'gestalt entity'. The Spillagers are extra-dimensional beings who 'spill' out constructed gateways into real space and 'pillage' inhabited worlds. They have ventral slaying claws and are ruled by an Empress. Their appearance is by all accounts repulsive, and fully transformed corpses of Spillagers tend to decompose and liquefy rapidly. They prepare their gateways on targeted worlds, assuming the identity and personality of chosen victims, who are destroyed and replaced by 'scouts'. The Doctor says they are a species to avoid 'at all costs'.
An Imaturitation is a living poultice that feeds upon projectile wounds, reabsorbing the bullet and healing scarred tissues. The Doctor has one in the TARDIS.
Nyssa can't ski and refuses an offer of cognac (see: 'Black Orchid') - she's unfamiliar with some Earth words, including 'poltergeist' and 'harlot'. The Doctor eats a ham sandwich. With him he carries some 'tea' containing a mild sedative (it's enough to put Alison under). In a golf bag (to match his seventh incarnation's jumper?) he carries tools used to detect energy emissions and psychic phenomena (see 'Technobabble'). Among these are a psi energy scanner and his 'Spillager detector', which is described as resembling 'an umbrella made of neon spaghetti that's been crossed with a phosphorescent jellyfish'. The Doctor keeps the living quarters on the TARDIS unacceptably warm and humid.
Links: Presumably this takes place directly after 'Land of the Dead' (Nyssa says 'it was worse than Alaska' and mentions the Permians and the Xeraphin ('Time Flight')).
Untelevised Adventures: The Spillager Empress recognises the Doctor, suggesting that they may have met before (certainly he would be unlikely to make detection equipment for something he is unfamiliar with).
Location: Tremayne School, the Swiss Alps, December 22nd 1963.
The Bottom Line: A novel and, at times, unnerving poltergeist adventure framed within a rare first person monologue. Some departures feature, notably in Davison's slightly less straight-laced Doctor and a travel weary (or should that be wary?) Nyssa. Perhaps most atypical for its era, the Doctor takes quite some time to finally make his entrance. The performances on the whole are very good, although the one deceased character leans towards caricature, and as in 'Phantasmagoria', the real villains tend to upset the spirit (ouch! - sorry) of the story.