The panoply of known physics required to fully determine the mechanism and phenomenology of core-collapse supernovae (CC SNe) is prodigious, and the feedbacks involved make the problem close to intractable. However, our understanding has been considerably enhanced via the insight gained from simulations on supercomputers. These simulations are among the largest and most complex numerical experiments ever undertaken. Neutrino transport approximations, spatial dimensionality, and affordable complexity in nuclear kinetics continue to be among the primary limitations on physical fidelity in core-collapse supernova simulations, even on today's petascale platforms. We have recently conducted a series of numerical experiments to examine the effects of several approximations used in multidimensional core-collapse supernova simulations. I will describe some of the results of these studies, including what approximations seem unrealistic and which are required for any future simulations if they hope to be definitive in any sense.