  We investigate the expected correlation between the weak gravitational shear
of distant galaxies and the orientation of foreground galaxies, through the use
of numerical simulations. This shear-ellipticity correlation can mimic a
cosmological weak lensing signal, and is potentially the limiting physical
systematic effect for cosmology with future high-precision weak lensing
surveys. We find that, if uncorrected, the shear-ellipticity correlation could
contribute up to 10% of the weak lensing signal on scales up to 20 arcminutes,
for lensing surveys with a median depth z=1. The most massive foreground
galaxies are expected to cause the largest correlations, a result also seen in
the Sloan Digital Sky Survey. We find that the redshift dependence of the
effect is proportional to the lensing efficiency of the foreground, and this
offers prospects for removal to high precision, although with some model
dependence. The contamination is characterised by a weakly negative B-mode,
which can be used as a diagnostic of systematic errors. We also provide more
accurate predictions for a second potential source of error, the intrinsic
alignment of nearby galaxies. This source of contamination is less important,
however, as it can be easily removed with distance information.
