The structure of aqueous LiCl, NaCl, KCl, CsCl, KF, and NaI solutions is calculated by molecular dynamics (MD) simulations of the frequently employed Dang force-field in SPC/E water. By using liquid state theory, we integrate the structure to obtain the electrolytes' osmotic coefficient phi and systematically investigate force-field quality and structural consequences to ion-specific bulk thermodynamics. The osmotic coefficients phi(chi) calculated from the exact compressibility route for the cation-Cl(-) force-fields match experiments for concentrations rho approximately < 2M, while NaI and KF parameters fail. Comparison of phi(chi) with phi(v) from the virial route, which relies on the pair potential approximation, shows that many-body effects become important for all salts above rho approximately 0.5M. They can be efficiently corrected, however, by employing a salt-type and rho-dependent dielectric constant epsilon(rho), generalizing previous observations on NaCl only. For physiological concentrations, rho approximately < 0.5M, the specific osmotic behavior is found to be determined by the short-ranged cation-anion pair potential only and is strongly related to the second virial coefficient of the latter. Presented methods and findings, based on simple integrations over the electrolyte structure, enable efficient MD force-field refinement by direct benchmarking to the sensitive electrolyte thermodynamics, instead to noncollective, single ion properties.