The Gravity Recovery and Climate Experiment (GRACE) was designed to measure variations in the Earth's gravity field from space at monthly intervals. Researchers have used these data to measure changes in water mass over various regions, including the global oceans and continental ice sheets covering Greenland and Antarctica. However, GRACE data must be smoothed in these analyses and the effects of geocenter motions are not included. In this study, we examine what effect each of these has in the computation of ocean mass trends using a simulation of ice melting on Greenland, Antarctica, and mountain glaciers. We find that the recovered sea level change is systematically lower when coefficients are smoothed and geocenter terms are not included. Assuming current estimates of ice melting, the combined error can be as large as 30--50% of the simulated sea level rise. This is a significant portion of the long-term sea level change signal, and needs to be considered in any application of GRACE data to estimating long-term trends in sea level due to gain of water mass from melting ice.