The importance of recent diffraction studies in establishing phase boundaries and isosteres for solid adsorbed monolayers of Kr and Xe on graphite is emphasised. Lattice parameter measurements give isosteres to ~0.6 % accuracy which can be used to test detailed statistical mechanical models of the solid layers. These models are developed using the most accurate rare gas potentials in conjunction with the cell model of the lattice dynamics. By concentrating on the solid-gas and solid-solid (registry-disregistry or localised-unlocalised) phase transitions, we show that : (i) the Sinanoglu-Pitzer (substrate-mediated) three-body energy is significant but approximately 0.4 times as large as originally proposed ; (ii) that misfit dislocations modify the form of the solid-solid phase transition, and that the Frank-van der Merwe form of the dislocation energy can be made to fit the observed (second-order) transitions reasonably well ; and (iii) that dislocations also modify diffraction intensities considerably