The celestial sources observed by geodetic very‐long‐baseline interferometry (VLBI), most of which are quasars, are resolved—they have a finite angular size as measured by the interferometer—yet modern geodetic VLBI analysis techniques still treat these sources as if they are point‐like. The errors introduced by source structure, the angular distribution of emission, have traditionally been believed to be a small fraction of the total measurement error budget. We analyzed the VLBI data of the CONT14 continuous observing campaign using standard geodetic and imaging techniques, along with an analysis of closures, combinations of interferometric measurements where the error contributions from station‐based effects such as tropospheric and ionospheric errors, clock and cable length errors, station position errors, and so on, cancel exactly, leaving only nonclosing errors, principally source structure and measurement noise. Our statistical analysis of the closure information, based on actual VLBI observations revealed that nearly half (40%) of the total geodetic VLBI error budget (in terms of variance) in CONT14 came from source‐structure effects, nearly the same variance as all station‐based error sources (43%). The remaining error due to other nonsource‐structure, nonclosing errors is also significant (17%). Previous studies, which were primarily simulation‐based, did not account for the full range of effects of source structure on real measurements. Source structure is a major contributor to errors in geodetic VLBI, and source structure must be taken into account in the entire VLBI operational chain, from scheduling to analysis, in order to mitigate its effects on astrometric and geodetic measurements.