We present a comparative test of three assumptions critical to the applicability of the multiple scattering (MS) method as it has been applied to the scattering of electrons by molecules. The MS method divides space into three regions: (I) atomic spheres, (II) an interatomic region between the atomic spheres and an outer boundary, and (III) an extramolecular region outside that boundary. The assumptions tested are (i) neglect of charge polarization except in region III, (ii) constancy of the potential in region II, and (iii) spherical symmetry of the potential in region III. We consider electron-N2 scattering at impact energies 5-50 eV. We show that the use of assumptions (i)-(iii) results in cross sections that differ by about 30% from those obtained from reasonably well converged close coupling calculations without such assumptions. The differences are up to a factor of two or three for the partial integral cross sections. We have not tested whether the multiple-scattering results are improved by using a more consistent treatment of region II.