  We present examples of non-Hausdorff, etale, essentially principal groupoids
for which three results, known to hold in the Hausdorff case, fail. These
results are: (A) the subalgebra of continuous functions on the unit space is
maximal abelian within the reduced groupoid C*-algebra, (B) every nonzero ideal
of the reduced groupoid C*-algebra has a nonzero intersection with the
subalgebra of continuous functions on the unit space, and (C) the open support
of a normalizer is a bissection.
