Admittingly I don't know all the original private eyes by heart, but once I do I will complete this section. So for now you got to live with what I learned from the DVD Booklet, my limited knowledge and imdb.com
Agatha Christie's famous crime-solving heroine who (at least in the Margret Rutherford movie versions) always is the winner
of some past championship to aid her in her quest, goes undercover and figures out the crime before anyone else even guesses what
is really going on.
In murder by death she is spoofed as Jessica Marbles witch is quite funny since in "Murder most foul" Miss Marples herself is called Marbles by a busy theatre director who didn't quite catch her name. Her solving of the "crime" is based on having knowledge about their host not mentioned to the viewer beforehand.
Another creation of Agatha Christie, the master detective, who might be best know to younger
audiences for appearing in the movie "Murder in the Orient Express". Where he appears as a surprise guest to
a long thought up murder plan.
So Milo Perrier of course states that he is Belgium and probably later in the line of inconsistency also says, referring to himself: Never underestimate a frenchman's nostrils. Presenting his solution is also marked by information withheld from the reader. Not that it really matters in this case.
Sam Spade is a creation of the author Dashiell Hammett, but probably better know as a character played by Humphery Bogart in the movie "The Maltese Falcon". Unfortunately I haven't seen that movie, yet.
Again Dashiell Hammett character's, who have appeared played by Myrna Loy and William Powell in the "Thin Man" movie series.