  The beta decay of molecular tritium currently provides the highest
sensitivity in laboratory-based neutrino mass measurements. The upcoming
Karlsruhe Tritium Neutrino (KATRIN) experiment will improve the sensitivity to
0.2 eV, making a percent-level quantitative understanding of molecular effects
essential. The modern theoretical calculations available for neutrino-mass
experiments agree with spectroscopic data. Moreover, when neutrino-mass
experiments performed in the 1980s with gaseous tritium are re-evaluated using
these modern calculations, the extracted neutrino mass-squared values are
consistent with zero instead of being significantly negative. On the other
hand, the calculated molecular final-state branching ratios are in tension with
dissociation experiments performed in the 1950s. We re-examine the theory of
the final-state spectrum of molecular tritium decay and its effect on the
determination of the neutrino mass, with an emphasis on the role of the
vibrational- and rotational-state distribution in the ground electronic state.
General features can be reproduced quantitatively from considerations of
kinematics and zero-point motion. We summarize the status of validation efforts
and suggest means for resolving the apparent discrepancy in dissociation rates.
