The effects of wavefront distortions induced by acoustic heterogeneities in breast thermoacoustic tomography (TAT) are studied. First, amplitude distortions are shown to be insignificant for different scales of acoustic heterogeneities. Next, the effects of phase distortions (errors in time-of-flight) in our numerical studies are investigated, and the spreads of point sources and boundaries caused by the phase distortions are studied. After that, a demonstration showing that the blurring of images can be compensated for by using the distribution of acoustic velocity in the tissues in the reconstructions is presented. Last, the differences in the effects of acoustic heterogeneity and the generation of speckles in breast TAT and breast ultrasound imaging are discussed.