While it is always dangerous to try and pinpoint The One Great Problem of Our Age in any field of endeavor, I think that you can make a pretty good case that, in modern programming, it is the question "What the hell is a Monad?"
For those who have been trouble getting the sense of it, I commend to you this recent blog article. It is long, but unusually clear and decently witty. It has the great advantage that the author only recently read himself into all of this stuff himself, so he has more sense of the problem. (Unlike most writeups, which eventually get to saying, "So it is obvious that..." when the reader doesn't find it at *all* obvious.)
Mind, it does still require that you know programming well (to understand *why* this stuff matters), and you need to follow closely. But it's one of the clearer descriptions I've seen.
Of course, it still doesn't answer *my* pressing question, which is what the hell Querki's Collections are, from a category-theory POV. But most people don't need to worry about that...