In Greek mythology Autolycus is the son of Olympian God Hermes and is generally presented as a master of theft, trickery and mischief, not unlike Flambeau.
The car Flambeau drives is a Jaguar XK120.
Flambeau says "So long, Marianne" which is also a song by Leonard Cohen.
Father Brown laments to Flambeau that the failure to return the cross will mean he is destined to be assigned to Coventry as his Bishop had warned. To this, Flambeau sarcastically responds that he hears they're building a new Cathedral in Coventry. The destruction of the cathedral in Coventry (the second) by the German Luftwaffe in World War 2 and the plan to build a third cathedral was well-known throughout Great Britain as a testimony to both the sacrifices and the resilience of the British people. The cornerstone was laid by Elizabeth II in March of 1956.