We present near-infrared and optical spectroscopic observations of a sample of 450$mu$m and 850$mu$m-selected dusty star-forming galaxies (DSFGs) identified in a 400 arcmin$^2$ area in the COSMOS field. Thirty-one sources of the 102 targets were spectroscopically confirmed at $0.2<z<4$, identified primarily in the near-infrared with Keck MOSFIRE and some in the optical with Keck LRIS and DEIMOS. The low rate of confirmation is attributable both to high rest-frame optical obscuration in our targets and limited sensitivity to certain redshift ranges. The high-quality photometric redshifts available in the COSMOS field allow us to test the robustness of photometric redshifts for DSFGs. We find a subset (11/31$approx35$%) of DSFGs with inaccurate ($Delta z/(1+z)>0.2$) or non-existent photometric redshifts; these have very distinct spectral energy distributions from the remaining DSFGs, suggesting a decoupling of highly obscured and unobscured components. We present a composite rest-frame 4300--7300AA spectrum for DSFGs, and find evidence of 200$pm$30 km s$^{-1}$ gas outflows. Nebular line emission for a sub-sample of our detections indicate that hard ionizing radiation fields are ubiquitous in high-z DSFGs, even more so than typical mass or UV-selected high-z galaxies. We also confirm the extreme level of dust obscuration in DSFGs, measuring very high Balmer decrements, and very high ratios of IR to UV and IR to H$alpha$ luminosities. This work demonstrates the need to broaden the use of wide bandwidth technology in the millimeter to the spectroscopic confirmations of large samples of high-z DSFGs, as the difficulty in confirming such sources at optical/near-infrared wavelengths is exceedingly challenging given their obscuration.
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