PSR J1022+1001 is a millisecond pulsar (MSP) that has exhibited significant variability in the shape of its pulse profile since its discovery in 1995. This variability has been seen to occur over short (~8 min) timescales as well as narrow frequency ranges. Quantifying this variability is necessary to achieve the high accuracy demanded by pulsar timing arrays like the North American Nanohertz Observatory for Gravitational Waves, (NANOGrav). It also has astrophysical implications for the pulsar emission mechanism. The NANOGrav 12.5-yr dataset contains 2 years of high-precision, polarization-calibrated observations of this MSP. We present a carefully-calibrated, multifrequency analysis of these data in order to characterize the nature, magnitude, and timescale of any pulse shape changes, develop methods to improve its timing precision, and evaluate its long-term stability.