Roots: Blade Runner (a rain-soaked undercity, while the upper classes live above, including a powerful individual with a real bird as a pet). Brave New World (the chips work in a similar way to soma)
Dialogue Triumphs: "Why does it always come down to the last minute?"
The Doctor's discussing his experience of violence with Vi: "I've seen things that would make you curl into a stuttering ball of denial for the rest of your life."
Double Entendres: If you're of a particularly dirty mind there's lots of amusement to be had in all the talk of "down below" and people getting "inside" others. Characters complaining that they've been "edited" is another, less smutty possibility, but let's just leave it with Vi:
"You're trying to arouse me, you want to get into my inner circle"
"Please remove that big filthy dirigible from my habitat"
Continuity: The Needle is a living construct which exists almost symbiotically with its inhabitants, the chipped 'upper class'. As a result the building looks after its inhabitants, expanding and shifting its dimensions (it was thought to once be hundreds of metres high) to accommodate the travel needs of its population — residents merely visualise their destination and the dimensions of the Needle accommodate their transit, saving the energy required for walking, and preventing people becoming lost. Living quarters are a routine affair, with little to distinguish between their various rooms, although mention is made of 'cradle rooms', presumably for the purpose of sleeping, although the terminology suggests something less adult.
The residents of the Needle themselves lead highly structured lives, their thoughts and passions largely inhibited by the Needle's AI interface, Whitenoise and the compulsory chip implanted in every resident of the Needle, and those who pass through the Sphere. The chips anticipate violent intentions and allow Whitenoise to remove the ability to put these into effect before they manifest inside the mind of the host — Whitenoise has a predictive temporal core built into its makeup in order to detect any potential for a violent intent. Possibly as a consequence of this level of control there is a black market in bloodspot simulation videos, and the construct features a special force field to prevent suicides. Intrigued by the possibility of 'natural' aggression resident Vi has a mask enabling her to experience the primitive emotions of her pet bird, Max. rarely, experience of aggression beyond Whitenoise's control is known unofficially as 'red lining' — legend persists of a Red Tape which contains recorded sequences of extreme violence committed under this state by Needle residents.
Below the Needle is the undercity, the home to those who have chosen to remain un-chipped. After the cost of running Whitenoise became untenable the Needle was privatised and retained a small maintenance crew. Those not wishing to remain in the building under Whitenoise's control were exiled without a chip — a wave of violence followed the distruption, but was quelled by use of population-wide sedatives. Though not quite an underclass, contact with residents in the Needle is made possible by aircraft such as dirigibles.
Celia arrived on the Sphere in a metallic time capsule from the 45th century, an era of technocrats and machine-driven life. By this era technology has allowed for biological temporal links between time craft and occupant, enabling the pilot to 'think like a machine'.
The drug Slow is a by-product recycled from the temporal elements within Whitenoise. It opens up one's synapses and allows for greater sensoral stimulus and works by creating a crystalline nervous system on top of a user's natural one; it then takes them out of time for two minutes by affecting their perception. The user can still interact with people but everything they do during those two minutes only 'occurs' once they've come down and the crystal crumbles, realigned them with true time. The result is that the user experiences those two minutes as compressed time. Sensation is increased under the influence of Slow (presumably during the coming down phase), and as the drug inherently adapts the user's biology as it is taken users can effectively heal at a faster rate as Slow repairs any damage later.
Before arriving on the Sphere the Doctor thinks the TARDIS's telepathic circuits were attacked by some violent disruption in the Vortex, and by relation the attack has affected him also. His Time Lord abilities allow him to mentally crumble the crystalline shell created by Slow around his own nervous system. He admits to Red that he has destroyed races, even whole worlds, and sometimes enjoyed doing it.
The Bottom Line: "To be so out of one's control is the ultimate luxury"
Science Fiction stories set in doped up, emotionally-inhibited communities are a dime a dozen, but few consider the threat posed not to those communities, but by them. As it stands Red is not the easiest to follow nor loaded with the most sympathetic characters, but it's well worth sticking around.