Linear and circular dichroic triplet-minus-singlet spectroscopy (LD(T-S) and CD(T-S)) are highly sensitive methods for determining the angles between the optical and microwave transition moments, the strength of molecular interactions, and band assignments of a wide range of biological systems. Both LD(T-S) and CD(T-S) spectra can in principle be measured via dichroic optically detected magnetic resonance (ODMR), a complex measurement method involving a sample with both linear and circular anisotropies, imperfect light modulation, possibly misaligned components, optical elements at low temperatures, and a partially polarized light source. We report a theoretical analysis of the influence of these effects on the measured spectra, via a Stokes-Mueller analysis of the optical system used for recording dichroic-ODMR spectra. From the theoretical results we develop and test experimental strategies to ensure the reliability and measurability of LD(T-S) and CD(T-S) spectra.