A repeating musical motif in this episode is the first and most recognizable 6 notes of the main theme from the James Bond film, "Thunderball (1965)", first heard at the beginning of "Dr. No" (1962).
The Doctor's "assumption" joke is a failed attempt to repeat an old joke about the word assume: "Never assume anything, because you make an ass out of u and me." (ass/u/me)
Joseph Long has previously appeared in Doctor Who in Series 4 Episode 11 "Turn Left".
The portrait of Pope Benedict IX on the entrance to the Hereticum bears a striking resemblance to Angelina Jolie.
The line that the scientist says to Bill and Nardole, "We'll all go together when we go," is from the Tom Lehrer song of the same name.