We monitored 13 moderate-luminosity active galactic nuclei at z = 0.36 to measure flux variability, explore feasibility of reverberation mapping, and determine uncertainties on estimating black hole mass from single-epoch data. Spectra and images were obtained with approximately weekly cadence for up to 4 months, using the Kast spectrograph on the 3 m Shane Telescope. In broad band we detect peak-to-peak variations of 9%-37% and rms variations of 2%-10%. The observed flux variability in the g' band (rest frame 2800-4000 A) is consistent with that in the r' band (rest frame 4000-5200 A), but with larger amplitude. However, after correcting for stellar light dilution using Hubble Space Telescope images, we find nuclear variability of 3%-24% (rms variation) with similar amplitudes in the g' and r' bands within the errors. Intrinsic flux variability of the Hβ line is also detected at the 3%-13% level, after accounting for systematic errors on the spectrophotometry. This demonstrates that a reverberation mapping campaign beyond the local universe can be carried out with a 3 m class telescope, provided that sufficiently long light curves are obtained. Finally, we compare the Hβ FWHM measured from mean spectra with that measured from single-epoch data, and find no bias but an rms scatter of 14%, mostly accounted for by the uncertainty on FWHM measurements. The propagated uncertainty on black hole mass estimates, due to the FWHM measurement errors using low S/N (10-15 pixel~(-1)) single-epoch spectra, is 30%.
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