We demonstrate, using a simple model, that, in the frame of muffin-tin-like potential, non-physical peculiarities appear in molecular photoionization cross-sections that are a consequence of “jumps” in the potential and its first derivative at some radius. The magnitude of non-physical effects is of the same order as the physical oscillations in the cross-section of a diatomicmolecule. The role of the size of these “jumps” is illustrated by choosing three values for it. The results obtained are connected to the previously studied effect of non-analytic behavior as a function of r, the potential V(r) acting upon a particle on its photoionization cross-section. In reality, such potential has to be analytic in magnitude and have a first derivative function in r. The introduction of non-analytic features in model V(r) leads to non-physical features - oscillations, additional maxima, and so forth - in the corresponding cross-section.