I've also see "haarig" used in the following way in a LEO forum. (I've translated the first two sentences):
Usage A is clear. Usage B is, too.
Haarig wird es, wenn die Wendung im übertragenen Sinn verwendet wird.
In a context like this, I would express the latter thought something like this:
It gets a little tricky if the expression is used in the figurative sense.
I haven't heard "a hairy problem/issue" used very often (though "a hairy math problem" makes perfect sense to me!) Since the OP mentions "ein haariges Problem" or "eine haarige Sache" specifically in the context of an unsolved technical problem, I'd probably express them as "a thorny problem/issue" here. Most often, though, "thorny" seems to be used to describe a question or issue that is particularly troublesome because it triggers very opinionated responses (which never happens on LEO, right?). ;c)
Related question for native German speakers:
Is "haarig" also used like "brenzlig" or "heikel" as in "a delicate subject/situation" or "a dicey proposition"? (Like "thorny," both "delicate" and "dicey" express the potential risk or danger involved, which seems similar to how "haarig" is sometimes used.)