Recently, this question was asked: http://www.physicsoverflow.org/22034/2d-ising-model-in-cft-and-statistical-mechanics?show=22034#q22034 . The question is basically asking "How do you identify the conformal field theory description of a given lattice model second order phase transition?"
This was a major unsolved problem in conformal field theory in the 2000s, but it might be solved now. On mathoverflow, it is standard to reject problems that are equivalent to famous conjectures (or at least accept any answer that shows the equivalence to the famous conjecture).
But in our case, since we have a review section, I think it might be appropriate to include unsolved problems as "hard research level questions". The answer to these questions would be automatically research level. Certainly answering this question would require a serious research effort.
We could implement this inside the reviews section, but I think it is a separate sort of thing--- it's an "unsolved problems" section. The rating for this can be "difficulty", and when we get an answer, this can modify the score by exp(difficulty^1/3), much as originality does in the review section.
It's an idea. I don't know where to put hard major research level questions like this. They will never get an answer on Q&A, there is no incentive there to do hard things like this.