The jackdaw is mentioned as the type of egg found by Father Brown and in the story he tells about "The Eagle and the Daw" whence this episode derives its title. The surname of the antagonist in this episode is Corven. The Latin name for the jackdaw is "Corvus monedula". This may be an inside joke perpetrated by the writers.
When Sargent Goodfellow tells Inspector Mallory that a witness reported a gunshot coming from Raymond Worrall's cottage, Mallory reluctantly gets up saying: "A policeman's lot is not a happy one". This is a line from the Policeman's Song in the comic opera "The Pirates of Penzance" by Gilbert & Sullivan (1879). It is part of the refrain: "When constabulary's duty's to be done, to be done, A policeman's lot is not a happy one.".