Like in any other semiconductor, point defects in transition-metal dichalcogenides (TMDs) are expected to strongly impact their electronic and optical properties. However, identifying defects in these layered two-dimensional materials has been quite challenging with controversial conclusions despite the extensive literature in the past decade. Using first-principles calculations, we revisit the role of chalcogen vacancies and hydrogen impurity in bulk TMDs, reporting formation energies and thermodynamic and optical transition levels. We show that the S vacancy can explain recently observed cathodoluminescence spectra of MoS2 flakes and predict similar optical levels in the other TMDs. In the case of the H impurity, we find it more stable sitting on an interstitial site in the Mo plane, acting as a shallow donor, and possibly explaining the often observed n-type conductivity in some TMDs. We also predict the frequencies of the local vibration modes for the H impurity, aiding its identification through Raman or infrared spectroscopy.