  We describe a many-body theory for interlayer dispersion forces between
weakly disordered atomically thin crystals and numerically investigate the role
of disorder for different layer-separation distances and for different
densities of induced electrons and holes. In contrast to the common wisdom that
disorder tends to enhance the importance of Coulomb interactions in Fermi
liquids, we find that short range disorder tends to {\it weaken} interlayer
dispersion forces. This is in line with previous findings that suggest that
transitioning from metallic to insulating propagation weakens interlayer
dispersion forces. We demonstrate that disorder alters the scaling laws of
dispersion forces and we comment on the role of the maximally crossed
vertex-correction diagrams responsible for logarithmic divergences in the
resistivity of two-dimensional metals.
