There is a portrait of William Hartnell on the wall at the U.N.I.T. safe house based on his appearance in "The Celestial Toymaker".
One of the leaders of the Zygon splinter cell was called originally Blinovitch, and had taken the form of Courtney Woods; in early drafts of Kill the Moon (2014), Blinovitch was revealed to be the surname Courtney would use as an adult. In the late stages, Blinovitch was the captive Zygon taken aboard the presidential aeroplane. At one point, she escaped her bonds and attacked the Doctor, only to be stopped by Osgood, who revealed herself to be a Zygon as well. This would have confirmed that the Osgood murdered by Missy in Death in Heaven (2014) was the human original.
There is a real town in New Mexico called "Truth or Consequences." The town's name was changed from "Hot Springs" on 31 March 1950 after Ralph Edwards, the host of the popular game show "Truth or Consequences," called for any town in America to do so - in celebration of the show's ten year anniversary.
The Doctor remarks that he once "snogged a Zygon". The Tenth Doctor kissed a Zygon impersonating Queen Elizabeth in The Day of the Doctor (2013).
Kate Stewart being unsure over which decade the Zygons first attempted to invade in, the '70s or the '80s, is in reference to the ambiguity over whether or not the original UNIT stories took place in the present or the near-future of their mid-70's air dates. The invasion that she specifically mentions was shown in Terror of the Zygons: Part One (1975).