Using light curves from the HATNet survey for transiting extrasolar planets we investigate the optical broad-band photometric variability of a sample of 27, 560 field K and M dwarfs selected by color and proper-motion (V-K>~3.0, mu>30mas/yr, plus additional cuts in J-H vs. H-Ks and on the reduced proper motion). We apply a variety of variability selection algorithms on the light curves to search for periodic and quasi-periodic variations, and for large-amplitude, long-duration flare events. To set the selection thresholds we conduct Monte Carlo simulations of light curves with realistic noise properties.