Colloidal quantum dots (CQDs) are highly versatile nanoscale optoelectronic building blocks, but despite their materials engineering flexibility, there is a considerable lack of fundamental understanding of their electronic structure as they couple within thin films. By employing a joint experimental-theoretical study, we reveal the impact of connectivity in CQD assemblies, going beyond the single CQD picture. High-resolution transmission electron microscopy (HR-TEM) demonstrates connectivity motifs across different CQD sizes and length scales and provides the necessary perspective to build robust computational models to systematically study the achievable degree of connectivity in these materials. We focused on state-of-the-art surface ligand treatments, taking into account both the degree of connectivity and nanocrystal orientation, and performed ab initio simulations within the phonon-assisted hopping regime. Importantly, both the TEM studies and our simulation results revealed morphological and electronic defects that could dramatically reduce optoelectronic performance, and yet would not have been captured within a single CQD model that neglects connectivity. We calculate carrier mobility in the presence of such defect states and conclude that the best achievable CQD assemblies for optoelectronics will require a modest degree of fusing via the {001} facet, followed by atomic ligand passivation to generate a clean band gap and unprecedentedly high charge transport.