The solid solution 0.5Ba(Ti0.8Zr0.2)O3-0.5(Ba0.7Ca0.3)TiO3 (BCZT) is a promising lead-free piezoelectric material with exceptionally high piezoelectric coefficients. The strong response is related to structural instabilities close to ambient temperature. We report here on temperature-induced anomalies in the dielectric, piezoelectric, and elastic coefficients and Raman spectroscopy of ceramic BCZT. The data indicate ferroelectric-ferroelectric structural phase transitions in this material in addition to those previously reported. An anomaly is also observed above the Curie temperature TC and is associated with the loss of polar structure that persists thirty degrees above TC.