In the market on Akhaten, the Doctor points out a Hooloovoo, a race first described in The Hitchhikers Guide To The Galaxy books as a "Super-intelligent shade of the colour blue".
The Doctor at one point mentions how the elements came together to form "shoes, and ships, and sealing-wax, cabbages, and kings" This is a direct reference to "The Walrus and The Carpenter" from "Through the Looking-Glass and What Alice Found There" by Lewis Carroll.
According to Matt Smith, there were "between 50 and 60 prosthetic aliens" in a scene set in an alien market.
The Doctor features minimally in the first act because Matt Smith was busy filming pick-ups or reshoots for Nightmare in Silver (2013).
In his speech, The Doctor includes the line "I walked in universes where the laws of physics were devised by the mind of a madman". This is a reference to The Three Doctors: Episode One (1972) in which the Time Lord Omega has been banished to the antimatter universe where his will is the only thing that maintains reality, but his exile has caused him to become insane.