We report on an ongoing project to investigate activity in the M dwarf stellar population observed by the Pan-STARRS 1 Medium Deep Survey (PS1-MDS). Using a custom-built pipeline, we refine an initial sample of $approx$ 4 million sources in PS1-MDS to a sample of 184,148 candidate cool stars using color cuts. Motivated by the well-known relationship between rotation and stellar activity, we use a multi-band periodogram analysis and visual vetting to identify 271 sources that are likely rotating M dwarfs. We derive a new set of polynomials relating M dwarf PS1 colors to fundamental stellar parameters and use them to estimate the masses, distances, effective temperatures, and bolometric luminosities of our sample. We present a catalog containing these values, our measured rotation periods, and cross-matches to other surveys. Our final sample spans periods of $lesssim$1-130 days in stars with estimated effective temperatures of $approx$ 2700-4000 K. Twenty-two of our sources have X-ray cross-matches, and they are found to be relatively X-ray bright as would be expected from selection effects. Our data set provides evidence that Kepler-based searches have not been sensitive to very slowly-rotating stars ($P_{rm rot} gtrsim 70$ d), implying that the observed emergence of very slow rotators in studies of low-mass stars may be a systematic effect. We also see a lack of low-amplitude ($<$2%) variability in objects with intermediate (10-40 d) rotation periods, which, considered in conjunction with other observational results, may be a signpost of a loss of magnetic complexity associated with a phase of rapid spin-down in intermediate-age M dwarfs. This work represents just a first step in exploring stellar variability in data from the PS1-MDS and, in the farther future, LSST.
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