The room-temperature structure of Na1/2Bi1/2TiO3 (NBT) ceramics was studied using several transmission electron microscopy (TEM) techniques. High-angle annular dark field imaging in a scanning TEM confirmed an essentially random distribution of Bi and Na, while electron diffraction revealed significant disorder of the octahedral rotations and cation displacements. Diffraction-contrast dark-field and Fourier-filtered high-resolution TEM images were used to develop a model that reconciles local and average octahedral tilting in NBT. According to this model, NBT consists of nanoscale twin domains which exhibit a(-)a(-)c(+) tilting. The coherence length of the in-phase tilting, however, is limited to a few unit cells and is at least one order of magnitude shorter than that of anti-phase tilting. Assemblages of such nanodomains are proposed to exhibit an average a(-)a(-)c(-) tilt system. Diffuse sheets of intensity in electron diffraction patterns are attributed to local cation displacements correlated along both < 111 > and < 100 > chains and suggest partial polar ordering of these displacements. Overall, the TEM data indicate significant chemical, cation-displacement and tilt disorder of the NBT structure at the nano and mesoscale and support the premise that the Cc symmetry recently proposed from powder diffraction refinements is an averaged best fit cell.