Thanks to the research efforts of Prof. John D. Ferry and others over the last several decades, the viscoelastic properties of polymers have been extensively determined. From this accumulated wisdom, polymer viscoelasticity has become a mature field of research. This basic knowledge of polymer viscoelasticity has made it possible to discern the deviations from the apparently established general rules that one of us (DJP) have found, continuing the tradition of exhaustive experimental measurement started by Prof. Ferry. From many experimental studies on polymers carried out in different laboratories, it has also become clear that these viscoelastic anomalies are general and not exceptional features. Therefore, they pose significant problems in the quest of a truly satisfactory understanding of polymer viscoelasticity. The Coupling Model (CM) has been used to rationalize a number of deviations from thermorheological simplicity. In the realm of polymer viscoelastic behavior, we consider first the local segmental motion that is responsible for the glass temperature and show that the CM provides a consistent description in either the modulus or the compliance representation. Next, we elucidate several viscoelastic anomalies which originate from the different viscoelastic mechanisms being thermorheologically complex. Finally, we revisit the original formulation of the terminal relaxation of entangled polymer chains using the CM. The neglect of the lateral nature of the constraints imposed on one chain by other chains in the original formulation leads to failure in explaining the shape of the terminal relaxation, although it is successful in other aspects. A new formulation, which includes the lateral nature of the constraints and its subsequent mitigation when the terminal relaxation is reached, has restored consistency of the prediction with the terminal relaxation of a monodisperse polyisoprene melt probed dielectrically. The results can describe also the experimental data of dilute poly isoprene probes in polybutadiene matrices and in networks.