One of the guards arresting The Doctor says "Tell it to the Newgate jailer," Newgate being the primary prison in London. On the US DVD, the subtitle says "Tell it to the new gate-jailer."
Ashildr states that it takes 10,000 hours to learn a skill, but this idea was first put forward by Professor K. Anders Ericsson in 1993 and popularised by Malcolm Gladwell in his 2008 book Outlier. Presumably, in the context of the Whoniverse, the Professor learned this idea from Ashildr.
(at around 30 mins) A radio mic pack is clearly dangling from under the breastplate of the parliamentary soldier who is pointing a gun at the doctor.
The Doctor blames the Terileptil for starting the Great Fire of London in The Visitation: Part Four (1982), when it was actually the Fifth Doctor who accidentally started the fire, although it was a Terileptil weapon that caused it to get out of control (again accidentally).