Department Q is a weird one because it goes with the trope of the acerbic hyper-competent guy, but then… actually, I don’t recall, is he actually incompetent? Or does he just not quite live up to his over-confidence.

Also it is sometimes hard with these detective shows because the screenwriters might want a character to be hyper-competent, but they are people too, limited in their ability to portray super-competent abilities. This can result in characters lucking their way into clues.