The title is a reference to The Man Who Fell to Earth (1976) starring David Bowie. Bowie was a major inspiration for the Twelfth Doctor (Peter Capaldi).
A few notes of the Doctor Who theme played on an electric guitar are heard when the Thirteenth Doctor appears for the first time.
Jodie Whittaker states "these legs used to be longer." Peter Capaldi was 6 feet tall, whereas she is 5 feet 5and 3 quarter inches tall. This makes her the shortest actor to play The Doctor.
Jodie Whittaker wore the exact same outfit that Peter Capaldi wore in the previous episode Twice Upon a Time (2017). Costume designer Ray Holman only had to buy boots in Whittaker's size, for health and safety reasons, as a lot of stunts and running were involved in this episode.
The character listed in the credits as "Tim Shaw" (because that's all The Doctor ever calls him) actually identifies himself several times as "T'zim Sha".