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Despite their application potential, the structure of CVD grown MoSe2 single layers remained relatively unexplored. Here we report the rotationally aligned CVD growth of MoSe2 single layers on graphite. Such MoSe2 layers are characterized by grain boundary structures with significantly reduced disorder and display a much lower grain boundary density compared to samples grown by MBE. We show that the grain boundaries of CVD MoSe2 on graphite are predominantly mirror twin boundaries (MTBs) and distinguish two classes of such MTBs based on their orientation relative to the zigzag directions of the MoSe2 lattice. By combining atomic resolution scanning tunneling microscopy (STM) and spectroscopy measurements with DFT calculations, we demonstrate that the predominantly present MTBs running along zigzag directions only slightly perturb the electronic structure of the MoSe2 sheet. This enables the CVD growth of large-area MoSe2 layers with high structural and electronic quality. Atomic resolution STM investigations also revealed a high density (1012 cm-2) of native point defects identified as Mo vacancies. Our DFT calculations predict that Mo vacancies in MoSe2 are magnetic, and their magnetic moment can be efficiently controlled electrically by tuning the Fermi level position.