There is a precession of the earth's axis of rotation -evidenced by astronomical observation- that is most easily explained by Newton's laws and a non-spherical earth.
@Ross Milikan suggested in a comment that this was not an answer because precession only shows that the moments about the principle axes are unequal - and this could be caused by a non-uniform distribution of mass inside a spherical earth.
That's not correct, in fact precession measurements (of orbiting satellites and the earth itself) provide our most accurate estimates of the figure of the earth. The distribution of density in the earth is constrained by seismological evidence, and support a generally 'onion skin' earth structure. Significant differences in uncompensated density distribution would give rise to non-hydrostatic stresses that would exceed the observational and experimental known strength of earth materials. Convection currents inside the earth give rise to non-hydrostatic stresses, but the amount of convection (to account for the entire moment) would be too vigorous to be consistent with observed geothermal heat flow. When we consider all the geophysical evidence available - the best explanation for J2 not being zero is that the shape of the earth is ellipsoidal and not a simple sphere.
Geophysics often arrives at it's best answers by searching for a model that can fit all the available information - gravity, heat flow, astronomical, and materials science. All real data sets are incomplete, and geophysicists are often trying to solve the 'inverse problem' anyway. More accurate answers are obtained by using a variety of independent data, than by using only one imperfect set.
Combining precession data and other geophysics data to calculate a physical model with which to estimate the polar and equatorial radii of earth is no less valid than measuring these with a transit and level (which is a practical impossibility anyway.)