We evaluate regions of parameter space in the minimal supergravity model where "unbounded from below" (UFB) or charge or color-breaking minima (CCB) occur. Our analysis includes the most important terms from the one-loop effective potential. We note a peculiar discontinuity of results depending on how renormalization group improvement is performed: One case leads to a UFB potential throughout the model parameter space, while the other typically agrees quite well with similar calculations performed using only the tree level potential. We compare our results with constraints from cosmology and naturalness and find a preferred region of parameter space which implies mg̃≲725 GeV, mq̃≲650 GeV, mW̃1≲225 GeV, and ml̃R≲220 GeV. We discuss the consequences of our results for supersymmetry searches at various colliding beam facilities.