What really made it interesting was the eccentric characters who made up the suspects. They were played by an eclectic group of character actors taken from the usual TV "repertory" group, the stars of other shows, former and even current movie stars, silent movie stars and even people from the independent film movement and the British theater and films, who were happy at the American TV exposure and quick paycheck they got for performing a few scenes on the show. You can see oddities like Basil Rathbone listening in pain to John Cassavetes doing a "beatnik Hamlet", Sterling Holloway trying to blackmail Cassavetes, William Demarest running a hotel for ex-Vaudvillians where an acrobatic act earns their keep by cleaning the chandeliers, a convention of police chiefs, each one modeled on a famous fictional detective, (it anticipates Neil Simon's "Murder by Death"), a fake Russian aristocrat who really isn't fake but figures that no one will believe him anyway so he pretends to be a fake, etc, etc.
Gene Barry, one of several Cary Grant imitators on TV at the time, (see Craig Stevens in "Peter Gunn", John Vivien in "Mr Lucky"), is perfect for the lead role, better than Dick Powell in the pilot, which was made two years before as part of Powell's anthology series. Powell would have played the lead in the show but died of cancer before he could undertake the role. They say acting is reacting and Barry is the greatest reactor in TV history, the perfect guy to play off of all the eccentrics. Gary Conway, who should have become a much bigger star, (he was later in "Land of the Giants"), Regis Toomey, the gorgeous Eileen O'Neill and Leon Lontoc offered excellent support.
Unfortunately, somebody, (Spelling? The network?), decided to junk the show by turning it into an under-financed, back-projected spy show. Burke suddenly abandoned LA and is mansion and Rolls-Royce to become a James Bond style agent who traveled the world for a secret government organization headed by someone called "The Man". It was a tepid version of "The Man From Uncle" and was placed opposite what turned out to be the greatest of all spy shows," I Spy", which was in color and filmed in actual locations around the world. The local ABC affiliate in Syracuse declined to even show "Amos Burke Secret Agent" and from what I saw of the episode in syndication, I can't blame them.
Amazingly, the program had a third incarnation and the by now fabulously successful Aaron Spelling brought it back in 1994. Burke was back in LA chasing crooks in his Rolls, but with a son to help him. they dusted off the old scripts for the new shows. Only occasionally did we see the old spark of creativity, such as a victim freezing to death on the hottest day of the year, an ambulance chasing lawyer getting run over by an ambulance, Ephraim Zimbalist Jr. as a greedy tycoon practicing his golf drive from the rook of his building, (who cares who it falls on?), and Brian Keith as an ex-marine turned romance novelist who puts on a dress to get in the mood to write. Still is was a lot better than the other new murder mystery which followed it, "Diagnosis Murder" with Dick Van Dyke. Unfortunately, the network kept the wrong one, (I doubt they cried about it, as it went on for years).
Without the original "Burke's Law", there would have been no "Diagnosis Murder". The original remains the best whodunit in TV history and one of the most entertaining shows of all time.