  Low-energy two-dimensional scattering is particularly sensitive to the
existence and properties of weakly-bound states. We show that interaction
potentials $V(r)$ with vanishing zero-momentum Born approximation $\int d^2r
V(r)=0$ lead to an anomalously weak bound state which crucially modifies the
two-dimensional scattering properties. This anomalous case is especially
relevant in the context of polar molecules in bilayer arrangements.
