  We study the wave equation with potential $u_{tt}-\Delta u+Vu=0$ in two
spatial dimensions, with $V$ a real-valued, decaying potential. With
$H=-\Delta+V$, we study a variety of mapping estimates of the solution
operators, $\cos(t\sqrt{H})$ and $\frac{\sin(t\sqrt{H})}{\sqrt{H}}$ under the
assumption that zero is a regular point of the spectrum of $H$. We prove a
dispersive estimate with a time decay rate of $|t|^{-\frac{1}{2}}$, a
polynomially weighted dispersive estimate which attains a faster decay rate of
$|t|^{-1}(\log |t|)^{-2}$ for $|t|>2$. Finally, we prove dispersive estimates
if zero is not a regular point of the spectrum of $H$.
