We have calculated the Landau level (projected) Green's functions and the density of states of a two-dimensional electron gas in a perpendicular magnetic field as effected by impurity scattering using several different approximations. The material parameters which we choose correspond to GaAs/GaAlAs heterostructures. At the simplest level we include the effects of Landau level mixing. An approximation to the vertex correction is then added to the calculation, and the results are compared. Finally we add the electron-electron interaction to the model in place of the vertex correction. In all cases, the electron spin is considered. We find that the vertex correction over-compensates for the screening and yields unreasonable results. In addition, we find the dynamic electron-electron screening to be a dominant factor in determining the properties of the system and bridges the gap between low and high magnetic field behavior.