  Interaction of waves with point and line defects are usually described by
$\delta$-function potentials supported on points or lines. In two dimensions,
the scattering problem for a finite collection of point defects or parallel
line defects is exactly solvable. This is not true when both point and parallel
line defects are present. We offer a detailed treatment of the scattering
problem for finite collections of point and parallel line defects in two
dimensions. In particular, we perform the necessary renormalization of the
coupling constants of the point defects, introduce an approximation scheme
which allows for an analytic calculation of the scattering amplitude and
Green's function for the corresponding singular potential, investigate the
consequences of perturbing this potential, and comment on the application of
our results in the study of the geometric scattering of a particle moving on a
curved surface containing point and line defects. Our results provide a basic
framework for the study of spectral singularities and the corresponding lasing
and antilasing phenomena in two-dimensional optical systems involving lossy
and/or active thin wires and parallel thin plates.
