Roots: Sounds a bit like something out of a fairy tale', says Mel and she'd be right for a story featuring a mysterious house in the heart of a mysterious forest (Hansel and Gretel, Goldilocks), two wicked sisters and their virtuous younger sibling (Cinderella), plus some trappings of fairy stories: ghosts, dragons, wishes and witches. Pulp serials ("and with one bound he was free"). The Doctor describes the sisters' cottage as 'Gaudi-esque.', Arsenic and Old Lace (murderous sweet old ladies.) Ghostbusters (the vacuum cleaner). Mildew quotes Servalan from Blake's 7 ("maximum power!"); The Odyssey (the Doctor compares Maria and Eliza to sirens) Danny the Champion of the World. 'Discretion is the better part of valour' (see Something Inside)
Goofs: Why should the vacuum cleaner have to be disposed of at the end of the story - surely it too is a product of the Wishing Beast's world and not a 300 year old relic from a crashed space ship?
Some of the regular and guest voices are a little recognisable as background 'ghost' voices (Colin Baker in particular.)
Technobabble: The sisters' vacuum cleaner has a proton filter which destabilises particles at the molecular level.
Double Disasters: Magrs goes macho - "Suck on this!"
Double Entendres: "Let me switch this from 'suck' to 'blow'"
Dialogue Triumphs: "My eyeballs melted in their sockets! One lump or two...?"
"Think 'cat', not 'tortoise'. And cats have all their best adventures at night"
"Curiosity and cats don't always mix well, and I'm feeling distinctly feline today"
"Magics, like ghosts, may appear to be inexplicable. But they are only unexplained."
Continuity: The Wishing Beast is described here as a highly-advanced 'creature of power and hunger' fugitive from some other dimension, and since hybridised with Daniel Applewhite (see: Links). Part of its nature is the box it arrived in which sustains it and Daniel. Having found its way to an asteroid in deep space it has created an environment to sustain life, including a forest, lake and house where the Applewhite sisters live.
The Applewhite children crashed their spaceship on the asteroid three hundred ago; at the time the sisters were in their late teens, while their brother Daniel was only a small child. Affected by the radiation they have each become transformed - the sisters, maddened by their experience and the struggle to survive off anything, have been driven insane while Eliza's burned eyes have developed 'lasers'. Answering a mysterious voice calling him one night Daniel came into contact with the Wishing Beast entity, merging with the creature and becoming (according to the Doctor) a hybrid creature, living off the life force of its victims and given the power to grant wishes.
According to Mildew every 'living essence' (i.e. soul) is composed of many layers, like an onion. The ghosts here have a slight physical presence, don't feel cold or see colour, and focus their remaining willpower in order to float above the ground and hold objects. There are fewer than a hundred here
The TARDIS can pick up psionic energy emissions (i.e, 'ghosts'). An alarm alerts the Doctor and Mel to the presence of lethal radiation after they land (c.f. The Daleks)
Mel is wearing legwarmers in this story. She doesn't believe in ghosts, and takes the Lord's name in vain a few times here.
The Doctor tells Mel that everyone has their own sad tale to tell, but when Mel asks about his, he changes the subject.
Links: More of the nature of the Beast and the box which sustains Daniel is revealed in The Vanity Box. The Talons of Weng-Chiang ('sleep is for tortoises - not said here, but implied by the Doctor)
Q.v. 'Ghosts and Apparitions' nb: this is the third story in which a 'ghost' interacts with the TARDIS.
Location: An unnamed skull-shaped asteroid in deep space.
The Bottom Line: "Wishes are the most powerful thing in the universe"
A fairy tale for Mel, though there's little chance of her being the heroine, unfortunately. Wishing Beast is slow going for a pretty light story, but it won't offend you either.