We present a first-principles study based on density functional theory of thermodynamic and electronic properties of the most important intrinsic defects in the semiconductor alloy Cd1-xZnxTe with x<0.13. The alloy is represented by a set of supercells with disorder on the Cd/Zn sublattice. Defect formation energies as well as electronic and optical transition levels are analyzed as a function of composition. We show that defect formation energies increase with Zn content with the exception of the neutral Te vacancy. This behavior is qualitatively similar to but quantitatively rather different from the effect of volumetric strain on defect properties in pure CdTe. Finally, the relative carrier scattering strengths of point defects, alloy disorder, and phonons are obtained. It is demonstrated that for realistic defect concentrations, carrier mobilities are limited by phonon scattering for temperatures above approximately 150 K.