The influence of mismatch on a coherent, stimulated scattering process including the effect of pump depletion is studied. The efficiency of the non-linear three-wave interaction exhibits marked threshold behaviour for increasing mismatch, a result which is a generalization of the corresponding behaviour of parametric processes. The analysis is applied to the stimulated scattering processes (notably stimulated Brillouin scattering) occurring in laser-plasma interactions, where severe mismatch may be caused by plasma inhomogeneity and/or differential Doppler shifts. By means of a simple physical model we obtain thresholds for stimulated scattering in inhomogeneous and differentially expanding plasmas, results which are in good agreement with those recently given by an alternative approach. In addition, expressions predicting the rise of the reflectivity above threshold are given.