The first pulsating ultraluminous X-ray source (PULX) to be identified is M82 X-2. After the discovery in 2014, NuSTAR observed the M82 field 15 times throughout 2015 and 2016. In this paper, we report the results of pulsation searches in all of these data sets and find only one new detection. This new detection allows us to refine the orbital period of the source and measure an average spin-down rate between 2014 and 2016 of ∼-6 × 10-11 Hz s-1, which is in contrast to the strong spin-up seen during the 2014 observations, representing the first detection of spin-down in a PULX system. Thanks to the improved orbital solution allowed by this new detection, we are also able to detect pulsations in additional segments of the original 2014 data set. We find a glitch superimposed on the very strong and variable spin-up already reported - the first positive glitch identified in a PULX system. We discuss the new findings in the context of current leading models for PULXs.