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$β$ 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$β$ 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$β$ profile is sensitive primarily to Eddington ratio, but that inclination effects play a role in some cases. (abridged) Comment: 19 pages, 11 figures, accepted in A&A