Zinc selenide (ZnSe) is a promising material for applications in quantum computing. Only recently, it was shown that fluorine-doped ZnSe may serve as a source for indistinguishable photons. We have studied both chlorine and fluorine point defects in ZnSe by means of first-principles density functional theory calculations. The incorporation of F or Cl, either isolated, pairwise, or in combination with Zn or Se vacancies, has been investigated thoroughly for a large variety of possible charge states. For the most important structures, computationally more demanding calculations, with a hybrid functional rather than the generalized gradient approximation for the treatment of electron exchange and correlation, have been carried out. This was found to have little effect on the energetical order of the defect, but considerably changes the absolute formation energies of the defects.