Protein-polyelectrolyte coacervates are self-assembling macroscopically monophasic biomacromolecular fluids whose unique properties arise from transient heterogeneities. The structures of coacervates formed at different conditions of pH and ionic strength from poly(dimethyldiallylammonium chloride) and bovine serum albumin (BSA), were probed using fluorescence recovery after photobleaching. Measurements of self-diffusion in coacervates were carried out using fluorescein-tagged BSA, and similarly tagged Ficoll, a non-interacting branched polysaccharide with the same size as BSA. The results are best explained by temporal and spatial heterogeneities, also inferred from static light scattering and cryo-TEM, which indicate heterogeneous scattering centers of several hundred nm. Taken together with previous dynamic light scattering and rheology studies, the results are consistent with the presence of extensive dilute domains in which are embedded partially interconnected 50-700 nm dense domains. At short length scales, protein mobility is unobstructed by these clusters. At intermediate length scales, proteins are slowed down due to tortuosity effects within the blind alleys of the dense domains, and to adsorption at dense/dilute domain interfaces. Finally, at long length scales, obstructed diffusion is alleviated by the break-up of dense domains. These findings are discussed in terms of previously suggested models for protein-polyelectrolyte coacervates. Possible explanations for the origin of mesophase separation are offered.