A single sheet of carbon, graphene, exhibits unexpected electronic properties that arise from quantum state symmetries, which restrict the scattering of its charge carriers. Understanding the role of defects in the transport properties of graphene is central to realizing future electronics based on carbon. Scanning tunneling spectroscopy was used to measure quasiparticle interference patterns in epitaxial graphene grown on SiC(0001). Energy-resolved maps of the local density of states reveal modulations on two different length scales, reflecting both intravalley and intervalley scattering. Although such scattering in graphene can be suppressed because of the symmetries of the Dirac quasiparticles, we show that, when its source is atomic-scale lattice defects, wave functions of different symmetries can mix.