In-plane temperature dependent dielectric behavior of BiFeO3 (BFO) as-grown thin films show diffuse but prominent phase transitions near 450 (±10) K and 550 K with dielectric loss temperature dependences that suggest skin layer effects. The 450 K anomalies are near the “transition” first reported by Polomska et al. [Phys. Status Solidi 23, 567 (1974)]. The 550 K anomalies coincide with the surface phase transition recently reported [Marti et al., Phys. Rev. Lett. 106, 236101 (2011)]. In addition, anomalies are found at low temperatures: After several experimental cycles, the dielectric loss shows a clear relaxor-like phase transition near what was previously suggested to be a spin reorientation transition (SRT) temperature (∼201 K) for frequencies 1 kHz < f < 1 MHz which follow a nonlinear Vogel–Fulcher (V–F) relation; an additional sharp anomaly is observed near ∼180 K at frequencies below 1 kHz. As emphasized recently by Cowley et al. [Adv. Phys. 60, 229 (2011)], skin effects are expected for all relaxor ferroelectrics. Using the interdigital electrodes, experimental data and a theoretical model for in-plane longitudinal and transverse direct magnetoelectric (ME) coefficient are presented.