Comets C/2001 Q4 (NEAT) and C/2002 T7 (LINEAR) passed within ~0.3 AU of Earth in April and May of 2004. Their tails were observed by the Earth-orbiting Solar Mass Ejection Imager (SMEI) during this period. A time series of photometric SMEI sky maps displays the motions and frequent disruptions of the comet plasma tails. Ephemerides are used to unfold the observing geometry; the tails are often seen to extend ~0.5 AU from the comet nuclei. Having selected 12 of the more prominent motions as "events" for further study, we introduce a new method for determining solar wind radial velocities from these SMEI observations. We find little correlation between these and the changing solar wind parameters as measured close to Earth, or with coarse three-dimensional reconstructions using interplanetary scintillation data. A likely explanation is that the transverse sizes of the solar wind perturbations responsible for these disruptions are small, lesssim0.05 AU. We determine the radial velocities of these events during the disruptions, using a technique only possible when the observed comet tails extend over a significant fraction of an AU. We find typical radial velocities during these events of 50-100 km s−1 lower than before or afterward. Time durations of such events vary, typically from 3 to 8 hr, and correspond to comet traversal distances ~106 km (0.007 AU). We conclude that these large disturbances are primarily due to ubiquitous solar wind flow variations, of which these measured events are a subset.