  Two dimensional transition metal dichalcogenides appear as good candidates
for gas sensing and catalysis. Here, by means of density functional theory, we
characterize the adsorption and dissociation of selected diatomic molecules
(CO, H$_2$, O$_2$, and NO) on the MoSe$_2$ monolayer. We consider that these
processes occur on the pristine $1H$-MoSe$_2$ monolayer and in the vicinity of
an isolated Se vacancy. The presence of Se vacancies both enhances the
molecular adsorption and reduces the energy needed for dissociation, making it
energetically favorable for the case of O$_2$ and NO molecules. For each case
we evaluate the effect that each adsorbate has on the electronic structure of
the MoSe$_2$ monolayer and the charge transfer that takes place between the
adsorbate and the surface. Remarkably, adsorption of either CO or NO at the Se
vacancy induces a finite spin-magnetization in the system that is spatially
well localized around the adsorbate and the three closest Mo atoms.
