First, I'm interested in stories where other characters--OCs, crossover characters, minor canon characters, whatever--respond to Jim and Blair's unorthodox partnership in realistic ways. Not so much ones where people shun or harass Blair because he has long hair and might be gay, but ones where other characters don't buy into the show's pararealistic conceit that a major crimes detective having an anthropologist for a partner is perfectly unremarkable. The response could be low-key hostility, bafflement, grudging realization that Blair's unusual perspective allows him to contribute--anything other than either handwaving or over-the-top hostility. Perfectly OK if this is a minor element in a good story that is mostly about something else.
Secondly, browsing over at epicrecs I have learned that apparently "too dumb to come in out of the rain"!Blair is a thing. A thing that I find on one level to be very silly, and on another level to be oddly compelling. Can you point me toward more of these? The ones I've already found are Food for Thought and Now That Larry's Gone... . (Edit: Actually, I guess New is one of these, too. Probably the least over-the-top of the trio.) In both of these examples, Blair's spectacular lack of common sense take the form of deciding that since he's out of money, he's just going to quit eating for several days (and go to considerable effort to hide this from Jim), but perhaps other examples may have him being self-sacrificingly dense in some other way.
(I don't imagine there are any where he literally doesn't come in out of the rain...but who knows, there could be. A story where he gets home early from some engagement, then decides that Jim probably wants some privacy, so he'll just sit on the stoop until he gets hypothermia would fit perfectly in this trope. Plus, as I'm sure we all know, the cure for hypothermia is nude snuggling. OK, yeah, I bet there is a story like this. Probably half a dozen.) Regardless, please point me toward your favorite examples of No Common Sense!Blair.