Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural framework for incorporating dynamic EEG generation models in source localization. Here, a recently developed inverse solution is introduced, which uses spatiotemporal Kalman filtering tuned through likelihood maximization. Standard diagnostic tests for objectively evaluating Kalman filter performance are then described and applied to inverse solutions for simulated and clinical EEG data. These tests, employed for the first time in Kalman-filter-based source localization, check the statistical properties of the innovation and validate the use of likelihood maximization for filter tuning. However, this analysis also reveals that the filter's existing space- and time-invariant process model, which contains a single fixed-frequency resonance, is unable to completely model the complex spatiotemporal dynamics of EEG data. This finding indicates that the algorithm could be improved by allowing the process model parameters to vary in space.