David Suchet performed all of the magic tricks Poirot is seen doing.
The time frame of this story can be speculated by the newspaper Japp places before Poirot with the headline "Bank Collapses. Demand Enquiry." There is a story below which mentions Sir Kingsley Wood as Minister of Health, a position he held from 1935 until 1938.
In his first scene, Kenneth Colley (Mr. Davenheim) puts on a record of Tchaikovsky's 1812 Overture. There is another connection between this actor and the 1812 Overture. In Ken Russell's biopic of Tchaikovsky, The Music Lovers (1971), the performance of the 1812 takes place as a stylised "pop video" in which Kenneth Colley plays a memorable part as Pyotr Ilyich Tchaikovsky's brother Modeste, manically counting money and firing the famous cannon that is an important part of the music.