The set and the business (write gag, read it, laugh, then frown, shake head, crumple it up and toss it onto the huge pile of paper) with Bernard Cribbins as the gag writer is almost identical to the set and business used a few years later for the beginning of the Monty Python skit about "The Funniest/Deadliest Joke in the World".
Clown makeups are copyrighted, and painting them on eggshells is actually one way that is used to document them for copyright purposes.
During the end tag, Steed is seen reading the Tintin comic book album "Le Lotus bleu" (1936) by Hergé in the original French.
Actor Julian Chagrin has exactly the same part in "Blow up" (1966), where he also plays a mime, a non-speaking part, and he's dressed almost quite identically as in this episode. Could be a tribute or in-joke.
One of the few plots in which Steed uses an alias (Gentleman Jack here) instead of his real name.