Polarization reversal in BiFeO3 (BFO) thin films in a parallel-plate capacitor configuration has been explored using piezo-force microscopy (PFM). Through-electrode mapping of the local piezoresponse allows for direct observation of the domain growth, which is being driven by a uniform electric field. Despite a good agreement between the measured switching curves and the classic Kolmogorov-Avrami-Ishibashi (KAI) model, the analysis of the polarization reversal maps reveals a more complicated switching behavior. A significant variation of the domain growth speed, strong asymmetry of the domain growth, blocked domain boundaries and presence of the insulated areas with nucleation-limited (NL) switching kinetics suggest a rather complex switching behavior that cannot be described by a simple KAI model.