The Time-Domain Spectroscopic Survey (TDSS) is an SDSS-IV eBOSS subproject primarily aimed at obtaining identification spectra of ∼220,000 optically variable objects systematically selected from SDSS/Pan-STARRS1 multi-epoch imaging. We present a preview of the science enabled by TDSS, based on TDSS spectra taken over ∼320 deg2 of sky as part of the SEQUELS survey in SDSS-III, which is in part a pilot survey for eBOSS in SDSS-IV. Using the 15,746 TDSS-selected single-epoch spectra of photometrically variable objects in SEQUELS, we determine the demographics of our variability-selected sample and investigate the unique spectral characteristics inherent in samples selected by variability. We show that variability-based selection of quasars complements color-based selection by selecting additional redder quasars and mitigates redshift biases to produce a smooth quasar redshift distribution over a wide range of redshifts. The resulting quasar sample contains systematically higher fractions of blazars and broad absorption line quasars than from color-selected samples. Similarly, we show that M dwarfs in the TDSS-selected stellar sample have systematically higher chromospheric active fractions than the underlying M-dwarf population based on their Hα emission. TDSS also contains a large number of RR Lyrae and eclipsing binary stars with main-sequence colors, including a few composite-spectrum binaries. Finally, our visual inspection of TDSS spectra uncovers a significant number of peculiar spectra, and we highlight a few cases of these interesting objects. With a factor of ∼15 more spectra, the main TDSS survey in SDSS-IV will leverage the lessons learned from these early results for a variety of time-domain science applications.