  Recent work using virial mass estimates and the quasar mass-luminosity plane
has yielded several new puzzles regarding quasar accretion, including a
sub-Eddington boundary on most quasar accretion, near-independence of the
accretion rate from properties of the host galaxy, and a cosmic synchronization
of accretion among black holes of a common mass. We consider how these puzzles
might change if virial mass estimation turns out to have a systematic bias. As
examples, we consider two recent claims of mass-dependent biases in MgII
masses. Under any such correction, the surprising cosmic synchronization of
quasar accretion rates and independence from the host galaxy remain. The slope
and location of the sub-Eddington boundary are very sensitive to biases in
virial mass estimation, and various mass calibrations appear to favor different
possible physical explanations for feedback between the central black hole and
its environment. The alternative mass estimators considered do not simply
remove puzzling quasar behavior, but rather replace it with new puzzles that
may be more difficult to solve than those using current virial mass estimators
and the Shen et al. (2008) catalog.
