  We try to identify the sources and systematics of the uncertainty of the
masses of the central black holes in active galactic nuclei (AGNs) which have
been obtained by reverberation-mapping methods. We characterize the broad
H$\beta$ emission-line profiles by the ratio of their full-width at half
maximum (FWHM) to their line dispersion, i.e., the second moment of the line
profile. We use this parameter to separate the reverberation-mapped AGNs into
two populations, the first with narrower H$\beta$ lines with relatively
extended wings, and the second with broader lines that are relatively
flat-topped. The first population is characterized by higher Eddington ratios
than the second. Within each population, we calibrate the black-hole mass scale
by comparison of the reverberation-based mass with that predicted by the bulge
velocity dispersion. We also use the distribution of ratios of the
reverberation-based mass to the velocity-dispersion mass prediction in a
comparison with a ``generalized thick disk'' model in order to see if
inclination can plausibly account for the observed distribution. We find that
the line dispersion is a less biased parameter in general than FWHM for black
hole mass estimation, although we show that it is possible to empirically
correct for the bias introduced by using FWHM to characterize the emission-line
width. We also argue that inclination effects are apparent in a small subset of
objects with the narrowest emission lines. Our principal conclusion is that the
H$\beta$ profile is sensitive primarily to Eddington ratio, but that
inclination effects play a role in some cases. (abridged)
