We investigate the effects of lateral viscosity variations (LVVs) on mantle circulation model predictions of the global geoid. The present study is motivated in part by earlier findings that LVVs due to stiff slabs in the lower mantle have a strong influence on the geoid, and that slabs in the lower mantle are perhaps no stronger than the ambient mantle. However, more recently, it has been argued based on global seismic tomography models that LVVs are a minor effect on the geoid. In the light of these seemingly contradictory results, we re-visit the problem of slab strength in the lower mantle. We substantiate that the geoid calculated from tomography is hardly affected by the presence of LVVs, whereas the geoid computed from global slab models yields a poor fit to the observed geoid when LVVs are considered. However, this degradation of fit only occurs for very long wavelengths of flow, indicating inherent differences between the slab and tomography models. We also investigate the effects on the geoid due to weak plate boundaries, strong cratonic keels, and a low viscosity region in the D″ layer due to post-perovskite. In addition to the geoid, we attempt to fit plate motions with a circulation model that has prescribed weak zones at plate boundaries. Motions are matched well and, taking into account LVVs, the geoid with appropriate surface velocity boundary conditions agrees with the observed geoid as well as for free slip cases.