Different surfaces and Schottky barriers of WSe2 single crystals have been investigated with photoelectron spectroscopy using synchrotron radiation. An acceptor level with E-A - E-V = 0.45 eV, known from the literature as an important defect level in WSe2, is identified and attributed to the non-van der Waals planes. The photovoltages obtained for the Schottky barriers prepared on UHV-cleaved selenium grown p-WSe2 single crystals depend on the lateral conductivity of the surface which is a function of metal-film thickness and morphology. Increased lateral conductivity leads to smaller photovoltages indicating laterally inhomogeneous losses of photoexcited carriers. It is suggested that the crystal quality of WSe2 single crystals, and thus, achievable conversion efficiencies of WSe2 solar cells, is strongly dependent on the transport agent used in chemical vapor transport growth.