Count Scarlioni (Julian Glover) kills Kerensky by using the time field generator to make him age very quickly, ending up as a skeleton. Glover later played a character in Indiana Jones and the Last Crusade (1989) who dies in a similar fashion. On the DVD commentary for this episode, Glover points this out himself.
Famous art forger Tom Keating would leave clues in his paintings as to their (non) authenticity. One of these would be to write "This Is A Fake" in white lead paint on the canvas before overpainting, so that x-rays would find the message. He had famously been put on trial and acquitted in 1977, so the Doctor's actions may have been a topical reference at the time of broadcast.
The Doctor writes his note to Leonardo da Vinci using backwards letters, then reads the letters in a mirror with them facing the right way; Da Vinci used this method of "mirror writing" in his journals so others could not read his works.
This episode was watched by 15.4 million viewers on its original transmission.
When The Jagaroth ( Julian Glover's character) explains that the Jagaroth landed on Earth 4 million years ago the Doctor said there was no life on Earth then. In actuality, fossilized cyanobacteria in Archaen rocks have been dated to 3.5 billion years ago.