We present an experimental investigation of the local dynamics and spatial diffusion of atoms in a rubidium optical lattice using polarization-selective intensity correlation spectroscopy in both the time and frequency domains. Autocorrelations of the circularly polarized components of the fluorescence light are shown to give access to the atomic dynamics in a single optical potential well. By contrast, cross correlations between opposite circular components of the scattered light provide information about atomic transport in the lattice through escape and recapture between neighbor potential wells.