Clones of bacteria possessing high-mutability rates (or mutators) are being observed in an increasing number of species. In a constant environment most mutations are deleterious, and hence the spontaneous mutation rate is generally low. However, mutators may play an important role in the adaptation of organisms to changing environments. To date, theoretical work has focused on temporal variability in the environment, implicitly assuming that environmental conditions are constant through space. Here, we develop a two--patch model to investigate how spatiotemporal environmental variability and dispersal might influence mutator dynamics. Environmental conditions in each patch fluctuate between two states; the rate of fluctuation varies in each patch at differing phase angles. We find that at low and intermediate rates of fluctuation, an increase in dispersal results in a decrease in the density of mutators. However, at high rates of environmental change, dispersal causes an increase in mutator density. For all frequencies of environmental fluctuation these trends are enhanced as the phase angle approaches 180[degrees]. We argue that future work, both empirical and theoretical, is needed to improve our understanding of how spatiotemporal variability impacts on mutator densities and dynamics.