Core-level photoemission peaks taken on several insulators with spatial resolution of 30-300 mu m rigidly shift in energy from place to place, most likely because of local charging effects. Such phenomena can affect the linewidth and the general lineshape of conventional, spatially integrated spectra even when a flood gun is used, which is one of the standard remedies against charging. This may require a critical revision of photoemission linewidths and lineshapes for many past experiments on insulators.