We outline two important effects that are missing from most evaluations of the dark matter capture rate in neutron stars. As dark matter scattering with nucleons in the star involves large momentum transfer, nucleon structure must be taken into account via a momentum dependence of the hadronic form factors. In addition, due to the high density of neutron star matter, we should account for nucleon interactions rather than modeling the nucleons as an ideal Fermi gas. Properly incorporating these effects is found to suppress the dark matter capture rate by up to 3 orders of magnitude for the heaviest stars.