One of the major difficulties encountered in modeling core collapse supernovae is obtaining an accurate description of the transport of neutrinos through the collapsed stellar core. The behavior of the neutrino distribution function transitions from an LTE distribution in the center of the core to a non-LTE distribution in the outer regions of the core. One method that has been recently employed in order to model the flow of neutrinos in 2-D models is the gray approximation. This approximation assumes that the neutrino distribution can be described by a function that is parameterized in terms of a neutrino temperature and a neutrino chemical potential. However, these parameters must be assumed. Furthermore, the parameters will also differ between the LTE and NLTE regions. Additionally, within the gray approximation the location at which the neutrino distribution function transitions from LTE to NLTE must be assumed. By considering a series of models where the LTE/NLTE decoupling point is varied we show that the outcome of the numerical models is critically sensitive to the choice of the decoupling point when the gray approximation is employed. We also examine the effects of the neutrino--electron scattering (NES) rate which is difficult to correctly formulate within the gray approximation. We show that NES has a dramatic affect on the the overall neutrino heating rate and the dynamics of the model. This result conflicts with the results of high resolution multi-group models which model neutrino transport without employing the gray approximation.