
There are a couple of things you find listening to OTR mysteries and detective shows... they can be more gruesome than movies were back then. They can also be a LOT more poorly written. I Love a Mystery in particular is one that I find willing to get its protagonists in an impossible situation... and then get them out of it in a completely impossible, you gotta be kidding me way.
So Yours Truly, Johnny Dollar really stands out for the quality of the writing, comparable to a good tough B movie of the period. If I had to name a second show I like a lot it would be The Whistler. It's kind of halfway in between Johnny Dollar and Inner Sanctum, in that it has a sinister narrator who seems to know everything (they're usually narrated in second person—"Yes, Doris Foonman, you thought you could just club your boss over the head with a pork loin and that would be smooth sailing for you!"), but the stories are fairly hardbitten and realistic, not supernatural-- and as noted, much more gruesome and doom-laden than the Production Code would allow. So I think they're of comparable quality, if not the same genre exactly.
I haven't heard a lot of either of these, but I've liked The Adventures of Sam Spade, with Howard Duff mostly, and Casey, Crime Photographer in its various incarnations. Also, for fun check out Bob & Ray's occasional sketches about Ace Willoughby, International Detective, with Ray doing a dead-on imitation of Bob Bailey's breathless Johnny Dollar.
Finally, there's a lot of streaming radio content at the BBC Radio site, which you can listen to usually for the month or so that it's available, but they repeat stuff a lot. There's a lot of Paul Temple and The Saint shows, as well as the inevitable Sherlock Holmes. More fun, there are have been pretty decent adaptations of Raymond Chandler with Toby Stephens, Maggie Smith's son, who manages a suitable period American accent most of the time; he also does James Bond (which is fitting in that he was a Bond villain in Die Another Day). Start here:
http://www.bbc.co.uk/radio/programmes/g ... ama/player" target="_blank