A variety of analyses of CuInSe2 have been performed using scanning tunneling microscopy. However, most of them fail to produce atomic resolution images. Our experimental data obtained on epitaxial thin films with various surface orientations and surface preparation methods suggest that this is not due to experimental errors. Scanning on adjacent GaAs surfaces reveals clear atomic resolution images. The results are interpreted as due to buried point defects in the material. Unlike the surface topography images, current-imaging tunneling spectroscopy data reveals features varying with atomic resolution. Furthermore the spectroscopy data shows changes in effective band edge positions significantly greater than are observed by optical measurements. These are proposed to be real band edge variations, which are screened electrostatically in optical measurements, which average over the exciton radius.