We report accurate energetics of defects introduced in GaN on doping with divalent metals, focusing on the technologically important case of Mg doping, using a model that takes into consideration both the effect of hole localization and dipolar polarization of the host material, and includes a well-defined reference level. Defect formation and ionization energies show that divalent dopants are counterbalanced in GaN by nitrogen vacancies and not by holes, which explains both the difficulty in achieving p-type conductivity in GaN and the associated major spectroscopic features, including the ubiquitous 3.46 eV photoluminescence line, a characteristic of all lightly divalent-metal-doped GaN materials that has also been shown to occur in pure GaN samples. Our results give a comprehensive explanation for the observed behavior of GaN doped with low concentrations of divalent metals in good agreement with relevant experiment.