We present new spectroscopic observations that are part of our continuing monitoring campaign of 88 quasars at z<0.7 whose broad H$beta$ lines are offset from their systemic redshifts by a few thousand km/s. These quasars have been considered candidates for hosting supermassive black hole binaries (SBHBs) by analogy with single-lined spectroscopic binary stars. We present the data and describe our improved analysis techniques, which include an extensive evaluation of uncertainties. We also present a variety of measurements from the spectra that are of general interest and will be useful in later stages of our analysis. Additionally, we take this opportunity to study the variability of the optical continuum and integrated flux of the broad H$beta$ line. We compare the variability properties of the SBHB candidates to those of a sample of typical quasars with similar redshifts and luminosities observed multiple times during the Sloan Digital Sky Survey. We find that the variability properties of the two samples are similar (variability amplitudes of 10-30% on time scales of approximately 1-7 years) and that their structure functions can be described by a common model with parameters characteristic of typical quasars. These results suggest that the broad-line regions of SBHB candidates have a similar extent as those of typical quasars. We discuss the implications of this result for the SBHB scenario and ensuing constraints on the orbital parameters.
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