I like my Sherlocks to be in good working order.
There has been much debate over that "high-functioning sociopath" line from BBC's Sherlock, but sociopath or no, if he's "high-functioning" who cares what his personal issues are? He's a Sherlock that works and works well.
At lunch today I was pondering those occasions when Sherlocks weren't in good working order, as some creators seem to have a fondness for breaking pretty things. Nicol Williamson's Sherlock from The Seven-Per-Cent Solution, for example, is a Sherlock completely built on disfunction . . . **SPOILER ALERT** . . . his Moriarty isn't even a real Moriarty. Peter Cook's Sherlock from the comedic version of The Hound of the Baskervilles is just painfully, painfully wrong, but it's done, at least theoretically, to be funny. Building a great Sherlock Holmes is so hard that a creator might be forgiven for giving him bad working parts, just so they don't have to risk not measuring up to the legend.
A truly stupid Holmes would definitely be a dysfunctional Sherlock, but I find myself letting Michael Caine's Sherlock from Without A Clue off the hook -- his Watson is so high-functioning as a detective that his character almost has to be an idiot. And we're still getting a Sherlock in good working order in that tale -- his name is just spelled "W-A-T-S-O-N."
Jonny Lee Miller's Sherlock from Elementary was actually assigned his Watson because he was dysfunctional. His Moriarty wasn't imaginary, like Nicol Williamson's, just . . . another **SPOILER ALERT** . . . the girlfriend he was sleeping with who faked her own murder, which is was so messed up that not only could he not solve it, he didn't even know he was being intimate with a criminal mastermind of the highest order. The Moriarty test would seem to be a good measurement of the functionality of a given Sherlock Holmes. A functional Sherlock battles a solid Moriarty and wins. Not without a cost, but, definitely, wins.
Perhaps the most dysfunctional Sherlock of all, especially with the Moriarty test, would be the one from Michael Dibdin's book The Last Sherlock Holmes Story (not yet done for the screen), but that tale's impact (and perhaps I should have thrown another "**SPOILER ALERT**" in here already) lies largely in the fact that you think you're reading about a fully functional Sherlock all along, only to find out otherwise in one horrific moment.
Broken Sherlock, however, is a character than cannot exist without fully functional Sherlock having drawn in the fans and the popularity sometime earlier. Had Conan Doyle originally created a broken Sherlock, nothing of what we know of as Sherlockiana would exist today, and we'd probably be reading some other writer who took a look at Doyle, like he did Poe, and went, "I think I can improve upon that sort of detective story."
A broken Sherlock will often get repaired in the course of his storyline, but one might as well be watching another detective who, over the course of his adventures, rises to the level of Holmes. That, at least, does not have the initial disappointment of not getting the marquee-advertised Sherlock Holmes that one expected.
Because really, a Sherlock in good working order is what we all want at some point, isn't it?