The exact solution of the spin-1/2 Falicov-Kimball model on an infinite-coordination Bethe lattice is analyzed in the regime of "classical" intermediate valence. We find that (i) either phase separation or a direct metal-insulator transition precludes intermediate valence over a large portion of the phase diagram, and (ii) within the intermediate valence phase, only continuous transitions are found as functions of the localized f-electron energy or temperature.