We have carried out the first nearside-farside (NF) analysis of angular scattering for molecular collisions in which the partial wave series for the scattering amplitude is expanded in a basis set of associated Legendre functions (of the first kind.) The practical implementation of the NF theory is described, which exploits in an essential way properties of associated Legendre functions of the second kind. The new concept of a restricted nearside-farside ((NF)-N-res) decomposition of the scattering amplitude is introduced, which takes into account the caustic structure of the associated Legendre functions. The (NF)-N-res theory is used to analyze polarization and degeneracy averaged differential cross sections for the Ar+N-2 collision system, treated as an atom+rigid rotor, The (NF)-N-res analysis always provides a clear physical interpretation of the scattering (except sometimes for scattering angles approximate to 0.180 degrees) for phenomena such as diffraction oscillations, potential rainbows, and rotational rainbows, as well as more complicated interference effects.