  We perform a theoretical study into how dipole-dipole interactions modify the
properties of superfluid vortices within the context of a two-dimensional
atomic Bose gas of co-oriented dipoles. The reduced density at a vortex acts
like a giant anti-dipole, changing the density profile and generating an
effective dipolar potential centred at the vortex core whose most slowly
decaying terms go as $1/\rho^2$ and $\ln(\rho)/\rho^3$. These effects modify
the vortex-vortex interaction which, in particular, becomes anisotropic for
dipoles polarized in the plane. Striking modifications to vortex-vortex
dynamics are demonstrated, i.e. anisotropic co-rotation dynamics and the
suppression of vortex annihilation.
