The dog's name's Bacchus. Very apt as Bacchus is the Roman God of wine (amongst other things) and the story takes place in a vineyard. Dionysus is mentioned at one point. Dionysus is the Greek equivalent to the Roman Bacchus
Lady Felicia sees Colonel Anthony bringing Lady Edna via wheelchair to the wine tasting party. She tells Father Brown that "He looks like a hero from an H. Rider Haggard novel." He quips back "In that case, does that make Lady Edna " She Who Must Be Obeyed?"" Horace Rumple of the TV series " Rumple Of The Bailey " (1978) privately calls his wife Hilda "She Who Must Be Obeyed". She never knew this but almost did when Rumple made a slip up but caught himself just in time. The nickname is a reference to the fearsome queen in H. Rider Haggard's adventure novel "She". It was published in book form in 1887.
The winery from which Gregoire received a letter of recommendation, Chateau Laponte, is the same winery from which Jane Milton gives Father Brown a bottle in the previous episode The Last Man (2015).
This episode represents yet another Harry Potter reunion. This time between Georgina Leonidas who played Katie Bell and 'Mark Williams'.