We investigate pump-probe electron detachment spectroscopy in a model system which is ideally suited to study coupled electronic and nuclear wave-packet dynamics. Time-resolved photoelectron spectra are calculated within the adiabatic approximation and a discretization of the detachment continuum. These spectra are compared to those which derive from a non-Born-Oppenheimer description and a numerically exact treatment of the detachment process. In this way it is possible to identify the influence of non-adiabatic effects on the spectra in a systematic way and also to test commonly applied approximations.