What is the problem with a rotating singularity? In most cases, people ask how can a point spin, resulting in a 'ringularity' as an answer. But I'm not quite sure why a point can't spin. After all, it's like saying how can something with mass have no volume, or how can a ringularity spin if each frame of its rotation is identical (since each point on the ring is identical).
 A: I guess that you're asking about the question How can a singularity in a black hole rotate if it's just a point?, and this highly upvoted answer.
The answer is just wrong. The angular momentum of a black hole is not "in" the singularity, but rather in the shape of the whole spacetime manifold, so there isn't really a problem.
The singularity of a nonrotating black hole isn't a point anyway. In the case of a Schwarzschild black hole, the causal structure of the spacetime is such that the $r\to 0$ limit should be treated as a sphere, or rather a cylinder when you include the $t$ dimension. The sphere doesn't have a well defined radius, but it's a sphere, not a point. In the case of a charged black hole, there is good reason to believe that there is a singularity at the inner event horizon, due to the so-called mass inflation instability, so the singularity does have a well-defined size and it isn't zero. The same instability exists in rotating black holes, so the theoretical ring singularity inside the inner horizon probably never exists in the real world. It scarcely matters, because the angular momentum is encoded in the spacetime outside the outer event horizon in any case.
Someone wrote a better answer to that question many years later. I just upvoted it and downvoted the other, but it's still 20 points short of being the top answer.
