The slang word "craic," pronounced "crack", is an Irish word with no direct translation in English, means good times had by all, pleasant conversation, gossipy news, enjoyable companionship, music, entertainment, and fun in general.
Phyllis Dare,(1890-1975), who is mentioned several times, was a great star as both an actress and singer during the Golden Age of British Theatre.
The £30 that the Dowager gives to Mosley in 1922 is worth ~£1346 ($1650) in 2022.
Anna chaperones Rose at a thé dansant in York; Thé dansants (French for "dancing tea") were dances held in the afternoon at which tea is served, and popular in the English countryside during the 1920s and 1930s.
When Michael says he wants to become a German citizen (so he can divorce his wife), Edith says the Royal Family "convulses the nation by ceasing to be German." King George V changed his family's name from Saxe-Coburg and Gotha to Windsor in 1917, five years before the setting of this episode. It's not clear what Edith means by "convulses the nation," as the name change proved to be very popular with the British public.