  We investigate $L^1(\R^2)\to L^\infty(\R^2)$ dispersive estimates for the
Schr\"odinger operator $H=-\Delta+V$ when there are obstructions, resonances or
an eigenvalue, at zero energy. In particular, we show that the existence of an
s-wave resonance at zero energy does not destroy the $t^{-1}$ decay rate. We
also show that if there is a p-wave resonance or an eigenvalue at zero energy
then there is a time dependent operator $F_t$ satisfying $\|F_t\|_{L^1\to
L^\infty} \lesssim 1$ such that $$\|e^{itH}P_{ac}-F_t\|_{L^1\to L^\infty}
\lesssim |t|^{-1}, \text{for} |t|>1.$$ We also establish a weighted dispersive
estimate with $t^{-1}$ decay rate in the case when there is an eigenvalue at
zero energy but no resonances.
