Simulations of galaxy formation are becoming increasingly realistic, both in the unresolved physical processes they model and in their ability to reproduce the properties of observed galaxy populations. However, we must not let this lead to a false sense of security. Instead, we must develop a deeper understanding of how numerical parameters — such as mass and force resolution — interact with the subgrid models employed by simulations, and establish the extent to which galaxy properties are affected by numerical choices. In this talk, I will discuss our recent work examining how these numerical parameters affect key structural and kinematic properties of simulated galaxies. I will also propose simple analytic criteria for identifying regions within galaxies — or galaxies within populations — that should be excluded from analysis. The talk should be of broad interest to researchers who occasionally use simulations, and particularly relevant to those whose research depends heavily on them.