Multistate reweighting methods such as the multistate Bennett acceptance ratio (MBAR) can predict free energies and expectation values of thermodynamic observables at poorly sampled or unsampled thermodynamic states using simulations performed at only a few sampled states combined with single point energy reevaluations of these samples at the unsampled states. In this study, we demonstrate the power of this general reweighting formalism by exploring the effect of simulation parameters controlling Coulomb and Lennard-Jones cutoffs on free energy calculations and other observables. Using multistate reweighting, we can quickly identify, with very high sensitivity, the computationally least expensive nonbonded parameters required to obtain a specified accuracy in observables compared to the answer obtained using an expensive "gold standard" set of parameters. We specifically examine free energy estimates of three molecular transformations in a benchmark molecular set as well as the enthalpy of vaporization of TIP3P. The results demonstrates the power of this multistate reweighting approach for measuring changes in free energy differences or other estimators with respect to simulation or model parameters with very high precision and/or very low computational effort. The results also help to identify which simulation parameters affect free energy calculations and provide guidance to determine which simulation parameters are both appropriate and computationally efficient in general.