Regarding Quarks: The Strong CP problem
This serious problem with quarks and the entire theory of Quantum ChromoDynamics needs to be more widely known and appreciated.
With QCD one expects some breaking of Charge/Parity symmetries. This is parameterized in something called the theta-angle. The most natural QCD value for theta is around 1. The empirically measured value is about 1 x 10^-9. The neutron is supposed to have an electronic dipole moment on the order of 10^-18 e.m, but the experimental upper limit is nearly a trillion times lower than that.
Physicists bow down to the golden calf of QCD, I have to ask: why? To me QCD looks like ad hoc model-building that has become ungainly and none too elegant. I think we can do much better.