Forward-backward semiclassical dynamics (FBSD) has emerged as a practical quasiclassical methodology for including important quantum mechanical effects in the initial state of a system, while retaining a classical description of the subsequent dynamics. FBSD expressions for time correlation functions or expectation values constitute rigorous stationary phase limits of the corresponding quantum mechanical quantities but can be evaluated with relatively little computational power. While allowing the inclusion of important effects such as zero point energy, the mixing of a quantum mechanical representation of the initial condition with a classical treatment of the dynamics is at least in principle inconsistent. In this paper we investigate various manifestations of this issue. Specifically, we examine the classical evolution of the quantized FBSD phase space density and the validity of the detailed balance condition in model systems. Our findings indicate that the practical consequences of the inconsistent quantum-classical treatment generally are of minor significance and suggest specific tests for checking the accuracy of FBSD calculations in polyatomic systems.