The general rule of thumb is that the “reader” of a mystery should be able to figure out the culprit before it is revealed. Mysteries are considered puzzles for the reader as well as the characters.
This actually puts them at odds with detective fiction, where the point is to watch a genius of some sort figure out things we couldn’t possibly. Think Sherlock Holmes, or his illustrious antecedent, Auguste Dupin. There are all sorts of examples, but the most profuse is the mystery. Agatha Christie, Dorothy Sayers, so on. The television mystery/detective drama adds a wrinkle, as it’s impossible to give the reader the clues without making it obvious. Thus the police procedural, such as Dragnet, CSI, Law & Order, even, to some extent, Bones (which I love, by the way). It’s a mix of the mystery and the detective, emphasizing the procedure rather than the intuitive leap.
These can get tiring, at least for me. However, there is a delight that is almost unfaltering for watching the genius at work. I can’t tell you how many times I’ve read every single Sherlock Holmes story (though I usually skip the middle section of A Study in Scarlet — I pointedly re-read the entire novel last year in Leslie Klinger’s delicious annotated edition). Thus comes our Monk and our Psych.
This is all due to a late-night episode of The Mentalist, which, when it is on-stride, is excellent, but can fall flat sometimes. Eventually these people would accept that Jane (the main character) can, indeed, do what he does.
I only know of two Japanese forms of all this: Detective Conan and Daughter of Twenty Faces (which, of course, calls to mind the writings of Edogawa Ranpo). Does more than this make it to Japanese television? The mystery, in all its guises, is and almost always has been a mainstay on American TV. Any other anime examples I should know about?

