Determination of the mechanical response of materials can be fraught with error if rheometer compliance is not properly taken into account. The resulting inaccuracies in the determined mechanical properties of the materials of interest can result in mistakes in material modeling, design, and theory. In the present work, we build on our previous report [K. Schröter, S. A. Hutcheson, X. Shi, A. Mandanici, and G. B. McKenna, J. Chem. Phys. 125, 214507 (2006)] and investigate the effects of instrument compliance that result from use of a commercial rotary rheometer and its fixtures on the determination of the dynamic shear and stress relaxation responses of glycerol, m -toluidine, and sucrose benzoate near to the glass transition regime. We revisit the procedure for compliance corrections presented in earlier work and correct dynamic shear data for these materials. We also present a new correction procedure to obtain shear stress relaxation curves from data that was obtained using this instrument. In addition, we broaden our consideration of compliance effects to materials, such as polymer melts, that have lower moduli than the simple glass formers previously considered. We discuss the possible errors for the viscoelastic response of glass-forming liquids and polymer melts or rubber networks that have been reported in the literature. A major purpose of the present work is to alert the community to possible problems in modulus values and relaxation functions obtained for a large number of materials for which rotary rheometers were used in a range where material stiffness (modulus and geometry effects) was comparable to the rheometer stiffness. Finally, we include recommendations for both experimental protocol and instrument design to avoid, minimize, or correct for compliance effects.