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The physical properties of anisotropic superconductors such as the critical temperature and other important properties depend sensitively on the electron mean free path. The sensitivity to impurity scattering and the resulting anomalies are considered a characteristic feature of strongly anisotropic pairing. These anomalies are usually analyzed in terms of s-wave impurity scattering which leads to universal pair-breaking effects depending on only two scattering parameters, the mean free path and the impurity cross section. We investigate here corrections coming from anisotropies in the scattering cross section, and find not only quantitative but also qualitative deviations from universal s-wave isotropic pair breaking. The properties we study are the transition temperature, quasiparticle bound states at impurities, and pinning of single-and double-flux lines by impurities.