Hexagonal boron nitride (h-BN) acts like a semiconductor vacuum to point defects enabling stable and controllable spin states at room temperature which qualifies them for quantum technological applications. To characterize their properties first-principles techniques constitute indispensable tools. The currently established paradigm for such solid-state electronic structure calculations is the density functional theory (DFT). Recently its variant, so-called DFT-1/2 method was introduced with the promise of accurate band gaps without a computational overhead with respect to ordinary DFT. Here, for the monolayer h-BN we contrast DFT and DFT-1/2 results for carbon substitutional impurities (CB, CN), boron and nitrogen single vacancies (VB, VN), divacancy, and Stone-Wales defects. Comparisons with more sophisticated, yet computationally costly techniques namely, hybrid functional DFT and the GW are also made, where available. From the standpoint of defect states embedded in the band gap region we demonstrate a clear advantage of DFT-1/2 in revealing the localized states otherwise buried within either the valence or conduction band continuum due to well-known gap underestimation syndrome of the standard DFT implementations. Thus, DFT-1/2 can serve for the rapid screening of candidate defect systems before more demanding considerations.