  We present a critical assessment of the calculation and uncertainty of the
$^{214}$Pb $\to$ $^{214}$Bi ground state to ground state $\beta$ decay, the
dominant source of background in liquid Xenon dark matter detectors, down to
below 1 keV. We consider contributions from atomic exchange effects, nuclear
structure and radiative corrections. For each of these, we find changes much
larger than previously estimated uncertainties and discuss shortcomings of the
original calculation. Specifically, through the use of a self-consistent
Dirac-Hartree-Fock-Slater calculation, we find that the atomic exchange effect
increases the predicted flux by $10(3)\%$ at 1 keV relative to previous
exchange calculations. Further, using a shell model calculation of the nuclear
structure contribution to the shape factor, we find a strong disagreement with
the allowed shape factor and discuss several sources of uncertainty. In the
1-200 keV window, the predicted flux is up to 20$\%$ lower. Finally, we discuss
omissions and detector effects in previously used QED radiative corrections,
and find small changes in the slope at the $\gtrsim 1\%$ MeV$^{-1}$ level, up
to $3\%$ in magnitude due to omissions in $\mathcal{O}(Z\alpha^2, Z^2\alpha^3)$
corrections and $3.5\%$ uncertainty from the neglect of as of yet unavailable
higher-order contributions. Combined, these give rise to an increase of at
least a factor 2 of the uncertainty in the 1-200 keV window. We comment on
possible experimental schemes of measuring this and related transitions.
