  The mass of the central black hole in many active galactic nuclei has been
estimated on the basis of the assumption that the dynamics of the broad
emission line gas are dominated by the gravity of the black hole. The most
commonly-employed method is to estimate a characteristic size-scale $r_*$ from
reverberation mapping experiments and combine it with a characteristic velocity
$v_*$ taken from the line profiles; the inferred mass is then estimated by $r_*
v_*^2/G$. We critically discuss the evidence supporting the assumption of
gravitational dynamics and find that the arguments are still inconclusive. We
then explore the range of possible systematic error if the assumption of
gravitational dynamics is granted. Inclination relative to a flattened system
may cause a systematic underestimate of the central mass by a factor $\sim
(h/r)^2$, where $h/r$ is the aspect ratio of the flattening. The coupled
effects of a broad radial emissivity distribution, an unknown angular radiation
pattern of line emission, and sub-optimal sampling in the reverberation
experiment can cause additional systematic errors as large as a factor of 3 or
more in either direction.
