We report on a systematic study of the thermodynamic, electronic and charge transport properties of high-quality single crystals of BaNiS$_2$, the metallic end-member of the quasi-twodimensional BaCo$_{1-x}$Ni$_x$S$_2$ system characterized by a metal-insulator transition at $x_{cr}=0.22$. Our analysis of magnetoresistivity and specific heat data consistently suggests a picture of compensated semimetal with two hole- and one electron-bands, where electron-phonon scattering dominates charge transport and the minority holes exhibit, below $sim$100 K, a very large mobility, $mu_hsim$ 15000 cm$^2$V$^{-1}$s$^{-1}$, which is explained by a Dirac-like band. Evidence of unconventional metallic properties is given by an intriguing crossover of the resistivity from a Bloch-Gruneisen regime to a linear$-T$ regime occurring at 2 K and by a strong linear term in the paramagnetic susceptibility above 100 K. We discuss the possibility that these anomalies reflect a departure from conventional Fermi-liquid properties in presence of short-range AF fluctuations and of a large Hund coupling.
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