This paper considers the downlink of a single-cell massive MIMO (multiple-input multiple-output) system with dual-polarized antennas at both the base station and users. We consider a channel model that takes into account several practical aspects that arise when utilizing dual polarization, such as channel cross-polar discrimination (XPD) and cross-polar receive and transmit correlations (XPC). We derive the statistical properties of the minimum mean squared error (MMSE) channel estimator for this model. Using these estimates for maximum ratio precoding, a rigorous closed-form downlink spectral efficiency (SE) expression is derived. We compare the SEs achieved in dual-polarized and uni-polarized setups numerically and evaluate the impact of XPD on the downlink SE.