We have used the zCOSMOS-bright 10k sample to identify 3244 Spitzer/MIPS 24 mum-selected galaxies with 0.06 mJy < S 24 mum lsim 0.50 mJy and I AB < 22.5, over 1.5 deg2 of the COSMOS field, and studied different spectral properties, depending on redshift. At 0.2 < z < 0.3, we found that different reddening laws of common use in the literature explain the dust extinction properties of ~80% of our infrared (IR) sources, within the error bars. For up to 16% of objects, instead, the Halpha lambda6563/Hbeta lambda4861 ratios are too high for their IR/UV attenuations, which is probably a consequence of inhomogeneous dust distributions. In only a few of our galaxies at 0.2 < z < 0.3, the IR emission could be mainly produced by dust heated by old rather than young stars. Besides, the line ratios of ~22% of our galaxies suggest that they might be star-formation/nuclear-activity composite systems. At 0.5 < z < 0.7, we estimated galaxy metallicities for 301 galaxies: at least 12% of them are securely below the upper-branch mass-metallicity trend, which is consistent with the local relation. Finally, we performed a combined analysis of the Hdelta equivalent width versus Dn (4000) diagram for 1722 faint and bright 24 mum galaxies at 0.6 < z < 1.0, spanning two decades in mid-IR luminosity. We found that, while secondary bursts of star formation are necessary to explain the position of the most luminous IR galaxies in that diagram, quiescent, exponentially declining star formation histories can well reproduce the spectral properties of ~40% of the less luminous sources. Our results suggest a transition in the possible modes of star formation at total IR luminosities L TIR &ap; (3 ± 2) × 1011 L sun.