We investigate shear flow instabilities using a recently derived constitutive law, designed for describing the rheology of entangled telechelic polymers. The continuum model displays shear banding, often accompanied by a strong elastic recoil in the transient response, which appears as an "apparent" wall slip. For certain parameters, the model also displays a novel apparent stick-slip behavior, giving rise to strong nonlinear oscillations in the stress response driven by a repeating cycle of elastic recoil followed by diffusive rehomogenization of the flow. We elucidate the detailed mechanism behind this oscillatory response, demonstrating that it arises from a competition between shear-induced breaking of sticky bonds, which leads to recoil and banding, and a diffusive rehomogenization of the flow. We discuss the relation between the apparent stick-slip in our continuum model and similar behavior in "true" wall slip. (C) 2017 The Society of Rheology.