Magnetic tunnel junctions employing FeCoB as the ferromagnet and MgO as a spacer layer exhibit high performance and are attractive for magnetic random access memory applications. Upon postdeposition annealing, B is observed to diffuse out of the FeCoB layers inducing crystallization of FeCo. It is known that a large proportion of B escapes into the adjacent tantalum underlayer. While diffusion of B into bulk MgO is known to be unfavorable, it is possible that B could diffuse into grain boundaries (GBs) in the polycrystalline MgO layer, affecting its electronic properties. In this paper, density functional theory is used to investigate the stability and electronic properties of oxygen vacancy and B interstitial defects at MgO GBs. We show that both types of defects exhibit increased stability at the GBs, and we introduce electronic states in the gap that could negatively impact performance. These predictions are consistent with recent experimental results, and we discuss further means to confirm the results experimentally using techniques such as x-ray or ultraviolet photoelectron spectroscopy.