Although there are many techniques that can detect bandgap states associated with point defects in the lattice, it is not routinely possible to determine the type of defect at submicron spatial resolution. Here we show that high-resolution electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope can locate and identify point defects with a resolution of about 10 nm in a wide-bandgap BAlN semiconductor. B interstitials, N vacancies, as well as other point defects have been experimentally detected using EELS and have been identified using density functional theory.