When Father Brown and the thief were down the well, Flambeau throws the rope down the well to stop them climbing out. Why didn't he just pull the rope up to the surface? And then Lady Felicia finds a rope ladder to climb down into the well. Why didn't they use that on the first place. I can't see Father Brown climbing down the rope, let alone up.
The Cadillac that Flambeau drives in New York has four headlamps. The series is set in 1953 but production-model Cadillacs didn't have quad headlamps until the 1957 model year.