The poem that Barnaby quotes starting "This is the weather the cuckoo likes" is Weathers by Thomas Hardy. He quotes most of verse one.
The threads of this episode weave through the arenas of computers and bicycles, which screenwriter Michael Russell humorously ties together at the beginning of the big race. The university choir sings Harry Dacre's song "Daisy Bell", which was programmed into an IBM 704 in 1961 at Bell Labs as the earliest demonstration of computer speech synthesis. (Which was witnessed by Arthur C. Clarke and featured in his book 2001: A Space Odyssey - thus appearing in Kubrick's film of the same name.) One of the most well remembered lines from the song itself, "You'll look sweet upon the seat / Of a bicycle built for two" - deftly brings the two themes together.
Two actors in this episode have played characters in different Poirot series. Philip Jackson played Inspector Japp in quite a few episodes of the David Suchet series and Jonathan Cecil played Hastings in the Peter Ustinov made for TV episodes ("Murder in Three Acts," etc.).
This is the only episode in series 12 that Barnaby's daughter Cully appears in.
One scene involves David Haig telling Jim Norton to kick someone "up the backside". Jim Norton played Bishop Brennan in the Father Ted episode Season 3, Episode 6: "Kicking Bishop Brennan Up the Arse".