A direct observation of the grain-boundary phases for several well-characterized hot-pressed PbMo₆S₈ samples were made by Auger electron spectroscopy. The surface elemental concentrations are completely different when compared to its bulk composition. The thickness of this altered composition is in the range 100–200 Å gradually increasing with increase in hotpressing temperature. Also, evidence of segregation of impurities, such as carbon and SiOₓ, to the grain-boundaries were noticed for some of the samples. Calorimetric experiments show a continuous broadening and a reduction in amplitude of the specific heat anomaly at Tc . This in terms of superconducting volume fraction indicates a Tc distribution in the range 9–15 K. Such an observation can be related to the local inhomogeneities with respect to the ternary composition, i.e., a deviation from ideal stoichiometry, PbMo₆S₈. The results are discussed in conjunction with X-ray diffraction, scanning electron microscope, and energy dispersive X-ray analysis. By considering the grain-boundary phases and the calorimetric observation of inhomogeneities, a plausible explanation is given for the low critical current densities in these materials.