  Relative phases of amplitudes for $D$ meson decays to a light pseudoscalar
meson $P$ and a light vector meson $V$ decaying to two pseudoscalar mesons will
lead to characteristic interferences on the three-body Dalitz plot. These
phases may be compared with predictions of a flavor-symmetric treatment which
extracts contributing amplitudes and their relative phases from a fit to $D \to
PV$ decay rates. Good agreement was found previously for the cases of $D^0 \to
K^- \pi^+ \pi^0$ and $D^0 \to \pi^+ \pi^- \pi^0$. The present work is devoted
to the decays $D^0 \to K_S \pi^+ \pi^-$ and $D^0 \to \pi^0 K^+ K^-$, for which
agreement is not found. Several suggestions are offered for this discrepancy.
