Cu–Zn–Pb brasses are popular materials, from which numerous industrially and commercially used components are fabricated. These alloys are typically subjected to multiple-step processing—involving casting, extrusion, hot forming, and machining—which can introduce various defects to the final product. The present study focuses on the detailed characterization of the structure of a brass fitting—i.e., a pre-shaped medical gas valve, produced by hot die forging—and attempts to assess the factors beyond local cracking occurring during processing. The analyses involved characterization of plastic flow via optical microscopy, and investigations of the phenomena in the vicinity of the crack, for which we used scanning and transmission electron microscopy. Numerical simulation was implemented not only to characterize the plastic flow more in detail, but primarily to investigate the probability of the occurrence of cracking based on the presence of stress. Last, but not least, microhardness in specific locations of the fitting were examined. The results reveal that the cracking occurring in the location with the highest probability of the occurrence of defects was most likely induced by differences in the chemical composition; the location the crack in which developed exhibited local changes not only in chemical composition—which manifested as the presence of brittle precipitates—but also in beta phase depletion. Moreover, as a result of the presence of oxidic precipitates and the hard and brittle alpha phase, the vicinity of the crack exhibited an increase in microhardness, which contributed to local brittleness.