  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--7300\AA\ 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.
