There are a number of references to the trial at the Crown Court. During the time that Father Brown is set, Crown Courts did not exist as they were created around 1971/72. In Father Brown's time, such matters would be dealt with at the Courts of Assize or Quarter Sessions.
George takes Mrs. McCarthy to the nice restaurant for a fish dinner. They have red wine, but the nice restaurant would almost certainly have recommended white wine with fish. Not a goof: The nice restaurant might recommend white wine, but it cannot force a patron to choose it.
When Iris Lightman leaves the village hall you can see a very modern electrical device in a plastic casing on the wall unavailable during the 1950s.