There are two that I can think of off the top of my head.

The first deals with singularities. Stephen Hawking gave us Hawking radiation that incorporates the mathematics of both General Relativity and Quantum field theory near the event horizon... and it makes sense. However, as you approach the singularity the maths become rather absurd. General relativity actually predicts its own failure upon reaching the singularity. I don't believe quantum theories have much to say about a singularity either. Thus the continuing research into quantum gravity.

The second is dealing with the gravitational field of particles. Given the Heisenberg Uncertainty Principle's statement on defining both the velocity and location of a particle, determining the gravitation field seems rather impossible. Fortunately, the gravitational field is so small, it can simply be ignored.