High-temperature cuprate superconductors display unexpected nanoscale inhomogeneity in essential properties such as pseudogap energy, Fermi surface, and even superconducting critical temperature. Theoretical explanations for this inhomogeneity have ranged from chemical disorder to spontaneous electronic phase separation. We extend the energy range of scanning tunneling spectroscopy on Bi(2+y)Sr(2-y)CaCu(2)O(8+x), allowing a complete mapping of two types of interstitial oxygen dopants and vacancies at the apical oxygen site. We show that the nanoscale spatial variations in the pseudogap states are correlated with disorder in these dopant concentrations, particularly that of apical oxygen vacancies.