We report on a pronounced redistribution of the local electronic density of states at the graphite surface, which is induced by the presence of low energy hydrogen-ion induced point defects. Scanning tunneling microscopy reveals standing waves in the local density of states, which are due to backscattering of electron wave functions at individual point defects. The superstructure thereby formed is directly related to the pointlike structure of the Fermi surface of graphite. For high defect density interference patterns are observed which sensitively change structure on the relative positions of the defects. These patterns could be reproduced by tight binding simulations of various defect distributions.