The main incompatibility is that QM predicts that all fields have a zero point energy associated with each mode. However, GR predicts zero point energy will cause spacetime to curve. However there are infinite modes in QM, so now using this in GR leads to all spacetime instantly collapsing. However we exist so this collapse hasn't happened. The solution is the elusive Quantum Gravity, something that physicists from Einstein, Feynman haven't been able to solve.