We obtain estimates of stellar atmospheric parameters for a previously published sample of 1777 relatively bright (9 < B < 14) metal-poor candidates from the Hamburg/ESO Survey. The original Frebel et al. analysis of these stars was only able to derive estimates of [Fe/H] and [C/Fe] for a subset of the sample, due to limitations in the methodology then available. A new spectroscopic analysis pipeline has been used to obtain estimates of Teff, log g, [Fe/H], and [C/Fe] for almost the entire dataset. This sample is very local - about 90% of the stars are located within 0.5 kpc of the Sun. We consider the chemodynamical properties of these stars in concert with a similarly local sample of stars from a recent analysis of the Bidelman & MacConnell weak-metal candidates by Beers et al. We use this combined sample to identify possible members of the suggested halo stream of stars by Helmi et al. and Chiba & Beers, as well as stars that may be associated with stripped debris from the putative parent dwarf of the globular cluster Omega Centauri, suggested to exist by previous authors. We identify a clear increase in the cumulative frequency of carbon-enhanced metal-poor (CEMP) stars with declining metallicity, as well as an increase in the fraction of CEMP stars with distance from the Galactic plane, consistent with previous results. We also identify a relatively large number of CEMP stars with kinematics consistent with the metal-weak thick-disk population, with possible implications for its origin.