The Mercury Orbiter Radio science Experiment (MORE) is one of the experiments onboard the ESA/JAXA BepiColombo mission to Mercury. Thanks to a state-of-the-art equipment, MORE will perform a very precise test of General Relativity, constraining the value of several Post-Newtonian parameters and other related quantities with an unprecedented accuracy. One of the main critical issues for the success of the MORE investigation is to correctly handle the systematic effects due to the instrumentation, which may significantly degrade the accuracy of the estimate, unless properly calibrated. In this work we evaluate, by means of a sensitivity analysis, the impact on the experiment given by systematic errors in the readings of the onboard accelerometer and in the end-to-end ranging system chain. The analysis shows that also small spurious effects in the range observables can be detrimental for the experiment, while the impact of the accelerometer is rather contained.