We present simultaneous dual-frequency Very Long Baseline Array 2 and 8 GHz observations of 225 of the 560 extragalactic sources for which positions were reported by Johnston and coworkers and which are now part of the International Celestial Reference Frame. These observations represent the third and final in a series of observations intended to obtain single-epoch images of the entire set of sources presented by Johnston and coworkers (1995, Cat. <J/AJ/110/880>) and, together with previously reported observations, bring the total number of sources observed to 389. As with previous papers in this series, we use these data to quantify the magnitude of the expected effect of intrinsic source structure on astrometric bandwidth synthesis Very Long Baseline Interferometry observations and to calculate a source "structure index" for the observed sources. The structure index can be used as an estimate of the astrometric quality of the sources. Based on this indicator, correlations between the observed radio structure and the astrometric position accuracy and stability of the sources have been found. These correlations indicate that the more extended sources have larger position uncertainties and are less positionally stable than the more compact sources.