It seems that mysteries, or at least detective stories, are so formula-driven that really the only elements that can be changed are the person of the detective, the physical setting and the time period. So even if you get, say, a book about a woman archaeologist detective in 19th century Egypt it's mostly the same as one about an ex-slave detective in the Roman Republic as some modern alcoholic sheriff in a Scandanavian country. (Once upon a time Peter Dickinson was playing with other elements--one book never resolved the question of whether a murder had occured at all--but that seems to happen now mostly in deliberately non-genre literary books such as Eco, Auster, etc.)
Now I'm pretty sure that this is the smug, reductive view - after all superhero comics look like just ridiculous power fantasies to outsiders (meaning most of the world) but attuned readers know that current Batman and Daredevil are very different things, even New Avengers and Mighty Avengers. (I'm not even talking about Grant Morrison's current "RIP" which is very different from rationality itself.)
But an article about "Crime fiction: Around the world in 80 sleuths" seems to support the reductive view. Whether Mongolia, South Wales or Brooklyn these come across as variations on a theme. Maybe that's because the title is mis-leading since these aren't just crime fiction but only detective fiction. In other words, The Sopranos wouldn't have qualified but CSI would have.
Still, there are a few writers that I will probably look up--Rafael Reig sounds particularly interesting--but what I really wanted was not books set in that location but books by writers from there. Not a British writer's novel about Mongolia but a Mongolian writer's novel about Mongolia (or even a Mongolian writer's novel about Britain). For all I know there aren't any Mongolian mysteries or maybe more likely none translated into English. But with movies it seems that there are three genres every country has - melodrama, low-brow comedy and crime stories. So I think it's a safe bet that if there are any Mongolian novels at all that at least a few of them are crime stories though perhaps not detective-oriented enough to have made this list.