Improvements in the analyses of Global Positioning System (GPS) observations yield resolvable millimeter to submillimeter differences in coordinate estimates, thus providing sufficient resolution to distinguish subtle differences in analysis methodologies. Here we investigate the effects on site coordinates of using different approaches to modeling atmospheric loading deformation (ATML) and handling of tropospheric delays. The rigorous approach of using the time-varying Vienna Mapping Function 1 yields solutions with lower noise at a range of frequencies compared with solutions generated using empirical mapping functions. This is particularly evident when ATML is accounted for. Some improvement also arises from using improved a priori zenith hydrostatic delays (ZHD), with the combined effect being site-specific. Importantly, inadequacies in both mapping functions and a priori ZHDs not only introduce time-correlated noise but significant periodic terms at solar annual and semiannual periods. We find no significant difference between solutions where nontidal ATML is applied at the observation level rather than as a daily averaged value, but failing to model diurnal and semidiurnal tidal ATML at the observation level can introduce anomalous propagated signals with periods that closely match the GPS draconitic annual (351.4 days) and semiannual period (175.7 days). Exacerbated by not fixing ambiguities, these signals are evident in both stacked and single-site power spectra, with each tide contributing roughly equally to the dominant semiannual peak. The amplitude of the propagated signal reaches a maximum of 0.8 mm with a clear latitudinal dependence that is not correlated directly with locations of maximum tidal amplitude.