As a skilled amateur cricket player (he plays for the Lord's Taverners) Peter Davison found it very difficult to play cricket badly, as required for the story in this episode. "It takes some skill to keep missing the ball like I did!"
In this story that looks back to the age of Cold War spying, Joyce Barnaby is seen reading the classic Cold War spy novel "Tinker Tailor Soldier Spy" by John Le Carré. This prompts DCI Tom Barnaby to reveal to Joyce that he had served in MI6, a.k.a. the Secret Intelligence Service that the story of "Tinker Tailor Soldier Spy" was about.
Peter Davison conspicuously bites a stick of celery. When he portrayed the fifth iteration of The Doctor in Doctor Who, he wore a stick of celery in his lapel, which would turn purple in the presence of "certain gases in the Praxis spectrum", to which he was allergic.