Native point defects, defect complexes, and oxygen impurities in BaCuChF were studied using density functional theory calculations, self-consistent thermodynamic simulations, and various experimental techniques. Unintentional p-type conductivity in BaCuChF is explained by the presence of copper vacancies with transition levels in the valence band. These acceptor-like defects are partially compensated by donor-like chalcogen vacancies with transition levels deep in the gap. Chalcogen vacancies also cause the experimentally observed sub-gap photoluminescence, optical absorption, and persistent photoconductivity in BaCuSF and BaCuSeF. In thermodynamic equilibrium, both copper and chalcogen vacancies have low formation enthalpies and are likely to form defect complexes among themselves and with fluorine interstitials. The calculated Fermi level pinning range in BaCuChF is narrow and located close to the valence band maximum. It makes BaCuChF a suitable transparent p-type contact layer for optoelectronic applications, but hinders attempts to fabricate transparent thin film transistors using this material. Oxygen-related defects do not affect bulk BaCuChF properties, but surface oxidation decreases the mean free path of free holes by almost an order of magnitude. ; Comment: 28 pages, 5 figures