We investigate, by means of first-principles calculations, the role of hBN point defects on the energetical stability and electronic structure of heterostructures composed of graphene atop hBN, rotated at angles of 13.17°, 9.43° and 7.34°. We consider, as possible point defects, boron and nitrogen vacancies and antisites, substitutional oxygen at the nitrogen site ON, substitutional carbon dimers, and nitrogen interstitials. The electronic and structural properties of all defects were analyzed. Among these, the most stable is ON, with negative formation energies at several possible rotation angles and chemical environments. Under such conditions, ON doping can raise the Fermi level of the neutral system by as much as 1 eV relative to graphene's Dirac point, reaching the band crossing between adjacent Dirac cones at the M point of the heterostructure Brillouin zone. This could lead to interesting electronic transport properties without the need for electrostatic doping.