Regarding the precision of quantum mechanics, I think that is true for all properties of particles except mass. The simplest quantum field theory has all particles massless, but clearly they are not. The origin of the masses demands explanation or else the standard model has a large number of arbitrary parameters. The mass (or inertia) of particles is interpreted as being due to interactions with Higgs bosons. This is analogous to treating the gravitational force as being due to interactions with gravitons, although there is not yet a quantitatively precise quantum theory of gravity. The properties of the Higgs boson may allow derivation of the masses of all particles, which would be a big step forward. Perhaps the most significant implication of a Higgs mass in the indicated range, however, is that it is consistent with the requirements of supersymmetry.