Given the basic parameters of a cosmic shear weak lensing survey, how well can systematic errors due to anisotropy in the point spread function (PSF) be corrected? The largest source of error in this correction to date has been the interpolation of the PSF to the locations of the galaxies. To address this error, we separate the PSF patterns into components that recur in multiple exposures/pointings and those that vary randomly between different exposures (such as those due to the atmosphere). In an earlier study we developed a principal component approach to correct the recurring PSF patterns. In this paper we show how randomly varying PSF patterns can also be circumvented in the measurement of shear correlations. For the two-point correlation function this is done by simply using pairs of galaxy shapes measured in different exposures. Combining the two techniques allows us to tackle generic combinations of PSF anisotropy patterns. The second goal of this paper is to give a formalism for quantifying residual systematic errors due to PSF patterns. We show how the main PSF corrections improve with increasing survey area (and thus can stay below the reduced statistical errors), and we identify the residual errors which do not scale with survey area. Our formalism can be applied both to planned lensing surveys to optimize survey strategy and to actual lensing data to quantify residual errors.