Think "Remington Steele" rather than "Hercule Poirot" for these, primarily, Art Deco stories. Tommy refers to mystery writers rather than movies but the idea is the same--well-dressed amateur pretending, comically, to be a professional private detective. In this case his partner, Tuppence, is even more expensively dressed, and hatted, and another complete novice. Upper crust Tommy has a background in Intelligence in WWI, when Tuppence, a clergyman's daughter and Tommy's childhood chum, was a nurse. It is true some of the mysteries aren't very mysterious but the series is impeccably staged, T & T are highly watchable and seem very much in love, young Albert is a lot of fun, and you get to imagine what you would do with a detective agency and a steady stream of money from your family. (You can also try to spot Britcom actors in the casts, or the times Britain's alleged xenophobia is brought up.)
"Secret Adversary" is a puzzle to me. I've read the book and studied the period but I can't imagine what unsigned treaty with the US when we were neutral, if it turned up some six years later in the UK, would be inevitably cause a general strike and a revolution. (The Atlantic Charter didn't do that in WWII.) And it's unsigned so why not just deny, deny, deny? Throughout the T & T series in the spy stories Christie hints but doesn't give us enough information to understand, all these years later and an ocean away, the gravity of the situation. Apparently Christie felt the UK was teetering on the brink of a Communist coup. She may have been warning the British public,--which is odd, really, in a book that spun off short stories that are lighthearted and humorous.