  We present preliminary results of several analyses searching for the effects
of CP violation and mixing in the decay of $D^0$ mesons. We find no evidence of
CP asymmetry in five different two-body decay modes of the $D^0$ to pairs of
light pseudo-scalar mesons: $A_{CP}(K^+ K^-) = (+0.05 \pm 2.18 \pm 0.84)% $,
$A_{CP}(\pi^+ \pi^-) = (+2.0 \pm 3.2 \pm 0.8)% $, $A_{CP}(K^0_{\rm S} \pi^0) =
(+0.1 \pm 1.3)%$, $A_{CP}(\pi^0 \pi^0) = (+0.1 \pm 4.8)%$, and $A_{CP}(K^0_{\rm
S} K^0_{\rm S}) = (-23 \pm 19)%$. We present the first measurement of the rate
of wrong-sign $D^0 \to K^+ \pi^- \pi^0$ decay: $R = 0.0043^{+0.0011}_{-0.0010}
\pm 0.0007$. We also describe a measurement of the mixing parameter $y_{CP}=
{\Delta\Gamma\over 2 \Gamma}$ by searching for a lifetime difference between
the CP neutral $K^{-}\pi^{+}$ final state and the CP even $K^+K^-$ and
$\pi^+\pi^-$ final states. Under the assumption that CP is conserved we find
$y_{CP} = -0.011 \pm 0.025 \pm 0.014$. Finally, we present our measurement of
the \dstarp width: $96 \pm 4 \pm 22$~k$e$V.
