We report the first nearside-farside (NF) analysis of angular scattering for an inelastic molecular collision in which the partial wave series for the scattering amplitude is expanded in a basis set of reduced rotation matrix elements d(mf,mi)(J)(theta), where theta is the scattering angle, J is the total angular momentum quantum number, and m(i),m(f) are initial and final helicity quantum numbers, respectively. The practical implementation of the NF theory is described in detail; it exploits in an essential way the properties of a function that we denote e(mf,mi)(J)(theta) and call a reduced rotation matrix element of the second kind. The caustic structure of d(mf,mi)(J)(theta) and e(mf,mi)(J)(theta) is taken into account via a restricted nearside-farside ((NF)-N-res) decomposition of the scattering amplitude. The (NF)-N-res theory is used to analyze polarization and degeneracy averaged differential cross sections for the Ar+N-2(j(i)=2,m(i)=0,+/-1,+/-2)--> Ar+N-2(j(f)=2,m(f)=0,+/-1,+/-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 theta approximate to0 degrees ,180 degrees) for phenomena such as diffraction oscillations and potential rainbows, as well as for more complicated (unnamed) interference effects. We also report results for some approximations to the (NF)-N-res theory. Mathematical properties of the e(mf),(J)(mi)(theta) required for the (NF)-N-res analysis are derived. (C) 2001 American Institute of Physics.