Anisotropic dynamics on the colloidal length scale is ubiquitous in nature. Of particular interest is the dynamics of systems approaching a kinetically arrested state. The failure of classical techniques for investigating the dynamics of highly turbid suspensions has contributed toward the limited experimental information available up until now. Exploiting the recent developments in the technique of differential dynamic microscopy (DDM), we report the first experimental study of the anisotropic collective dynamics of colloidal ellipsoids with a magnetic hematite core over a wide concentration range approaching kinetic arrest. In addition, we have investigated the effect of an external magnetic field on the resulting anisotropic collective diffusion. We combine DDM with small-angle x-ray scattering and rheological measurements to locate the glass transition and to relate the collective short- and long-time diffusion coefficients to the structural correlations and the evolution of the zero shear viscosity as the system approaches an arrested state.