The reference to "Home Rule" in dialogue, refers to the long troubled political history, between the UK and Ireland, that would eventually lead to the Republic of Ireland.
The Disarmament Conferences (seen on a newspaper in this episode, hanging on a post) were a series of conferences known collectively as the Conference for the Reduction and Limitation of Armaments. The conferences were held in Geneva which began in 1932 and did not end until 1934. There were no disarmament conferences held in Paris, as the show implies, although the appointed British Prime Minister Ramsay MacDonald (PM from 1929 to 1935) did have diplomatic missions to Paris, during that time frame. There is the Paris Peace Conference but that was at the end of the Great War and disarmament was mentioned, but was not the primary Disarmament Conference listed above.
Poirot's home telephone number is revealed as TRAFALGAR (872) 8317
DavidHorovitch, who plays commander Daniels also play Inspector Slack in several Miss Marple episodes.