Inaccuracies in the atomic shell model due to the neglect of electron correlation and some relativistic effects are examined. The asymptotic behavior of atomic valence electrons is considered, and the accuracy of the asymptotic coefficient of the electron wave function is evaluated with account for the model errors. The coupling of the electron orbital momenta and spins in atomic particles, molecules, and colliding particles is discussed. The resonant charge exchange process is analyzed in terms of the asymptotic theory, with the inverse of the typical ion-atom separation being used in the small-parameter expansion of the cross section. The influence of atomic shell model errors — via the valence electron asymptotic coefficient — on the accuracy of the charge exchange cross section is discussed. The relation between the cross section and the specifics of the moment addition law for an ion-atom collision event is elucidated. The accuracy-estimated values of cross sections for the slow-collision resonant charge exchange are given for most elements in the periodic table.