Mean surface geostrophic ocean currents may be calculated from the Mean Dynamic Topography (MDT), estimated as the difference between a mean sea surface height (MSS) calculated from radar altimeters and a reference geoid height. A review of the most widely used geoids is presented. The difference between the third release of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) geoid and three earlier geoids (the Earth Geopotential Model 1996 [EGM96], one of the geoids obtained by the Gravity Recovery and Climate Experiment [GRACE05], and the Earth Gravitational Model 2008 [EGM2008]) is computed and interpreted as an ‘artefact’ MDT, i.e. a misfit when non-accurate geoid models are used to calculate the ocean MDT and related geostrophic currents. These results are contrasted with the MDT computed by comparing the GOCE geoid with the MSS distributed by Collecte Localisation Satellites in 2001 (CLS01). The comparison shows that there was a strong influence of altimetry measurements in the construction of the EGM96 geoid, i.e. the artefact MDT calculated using EGM96 shows a high resemblance to the MDT computed using the MSS CLS01 field, both considering GOCE as the reference geoid. The correlation disappears largely, but not completely, for the two most recent geoids; in particular, the MSS has greater global influence on GRACE05 than on EGM2008 although the latter does better at latitudes of less than 60° and is more useful for reproducing the intense western boundary currents. The results show that EGM96 may lead to significant errors in the spatial gradients of MDT (for latitudes of less than 60° the global root mean square is 0.2422 m) and therefore in the geostrophic surface velocities. When the spatially averaged GRACE and EGM2008 geoids are used for latitudes of less than 60°, the global MDT root mean square is substantially reduced.