  We consider the influence of planar ``magnetic" imperfections which destroy
the local magnetic order, such as Zn impurities or $Cu^{2+}$ vacancies, on the
low temperature properties of the cuprate superconductors. In the unitary
limit, at low temperatures, for a $d_{x^2-y^2}$ pairing state such
imperfections produce low energy quasiparticles with an anistropic spectrum in
the vicinity of the nodes. We find that for the $La_{2-x}Sr_xCuO_4$ system, one
is in the {\em quasi-one-dimensional} regime of quasiparticle scattering,
discussed recently by Altshuler, Balatsky, and Rosengren, for impurity
concentrations in excess of $\sim 0.16\%$ whereas YBCO$_7$ appears likely to be
in the true 2D scattering regime for Zn concentrations less than $1.6\%$. We
show the neutron scattering results of Mason et al. \cite{Aeppli} on
$La_{1.86}Sr_{0.14}CuO_4$ provide strong evidence for ``dirty d-wave"
superconductivity in their samples. We obtain simple expressions for the
dynamic spin susceptibility and $^{63}Cu$ spin-lattice relaxation time,
$^{63}T_1$, in the superconducting state.
