Epitaxial attachment of quantum dots into ordered superlattices enables the synthesis of quasi-two-dimensional materials that theoretically exhibit features such as Dirac cones and topological states, and have major potential for unprecedented optoelectronic devices. Initial studies found that disorder in these structures causes localization of electrons within a few lattice constants, and highlight the critical need for precise structural characterization and systematic assessment of the effects of disorder on transport. Here we fabricated superlattices with the quantum dots registered to within a single atomic bond length (limited by the polydispersity of the quantum dot building blocks), but missing a fraction (20%) of the epitaxial connections. Calculations of the electronic structure including the measured disorder account for the electron localization inferred from transport measurements. The calculations also show that improvement of the epitaxial connections will lead to completely delocalized electrons and may enable the observation of the remarkable properties predicted for these materials.