According to the front page article in The New York Times the essence
of the neutrino experiment is in the comparison of what comes from
above with what comes from below (after traveling through Earth). The
orientation of light cones, from the Cerenkov effect, helps to
distinguish one direction from another.
They say that the mass of the neutrino can be as large as several eV.
This helps to answer the question about measuring it directly. Even if
the mass of a neutrino were 100 eV, measuring it directly would be
impossible. The accuracy of atomic mass measurements, as far as my table
shows, is not better than several hundreds of eV. But who knows, given
enough motivation mass spectrometrist may be able to generate more
accurate data.
Ludwik Kowalski