Compressible supercritical fluids exhibit extended density inhomogeneities which, due to their collective many-particle nature, fluctuate only very slowly, a phenomenon known as "critical slowing down." Our computations demonstrate that these slowly fluctuating inhomogeneities may remain effectively frozen on the time scale of fast dynamic processes such as solute vibrational relaxation. Furthermore, we find that a given solute molecule may experience any of a broad distribution of effectively static local solvent environments and that each solute's dynamical behavior will be controlled by its own local solvent environment. Consequently, an ensemble of solute molecules will relax with a correspondingly broad distribution of lifetimes. Although such inhomogeneous broadening effects are expected in amorphous solids and glasses, this is the first confirmation of their presence in supercritical fluids.