  The spectral properties of the Wilson-Dirac operator in 2-dimensional QED
responsible for the appearance of exceptional configurations in quenched
simulations are studied in detail. The mass singularity structure of the
quenched functional integral is shown to be extremely compicated, with multiple
branch points and cuts. The connection of lattice topological charge and
exactly real eigenmodes is explored using cooling techniques. The lattice
volume and spacing dependence of these modes is studied, as is the effect of
clover improvement of the action. A recently proposed modified quenched
approximation is applied to the study of meson correlators, and the results
compared with both naive quenched and full dynamical calculations of the same
quantity.
