Edward Clayton (Malcolm Sinclair) is the name of one of the characters in this episode. Edward Clayton is also the name of the actor who plays Rouse.
At 38:50, the young lad Hastings was talking to was eating a plate of Jellied eels, a popular traditional working-class English dish since early 1900's that consists of chopped eels boiled in a spiced stock that is allowed to cool. Eel is a naturally gelatinous fish so the cooking process releases collagen into the liquid which solidify on cooling to form a jelly. It is eaten cold.
Hastings & Poirot pass a portrait when leaving the Military Club after meeting Colonel Curtis (the camera actually moves in on it) and again later, when Poirot visits the club a second time. This same portrait is used to represent General John Laverton Arundell in Dumb Witness (1996).
Major Rich wears the necktie of the Brigade of Guards.