Earth's precession and nutations are mainly generated by the luni-solar tidal torque. Diurnal retrograde variations in the atmospheric and oceanic angular momenta in an Earth-fixed reference system induce some additional nutation motions. Observed precession and nutations are derived from very long baseline interferometry (VLBI) data, assuming that the direction of the observed quasars are fixed in space. In this study, we consider the effects of two possible causes for explaining discrepancies between the observed nutations and those modeled in MHB2000 (model adopted by the International Astronomical Union): (1) the time variations in the atmospheric (and potentially oceanic) forcing of the nutations, of the free core nutation (FCN), and of the free inner core nutation (FICN), and (2) the possible contamination of VLBI-derived nutation amplitudes by apparent changes in the directions of the extragalactic radio sources. The robustness of MHB2000 is tested by perturbing some of the parameters and assessing the validity of the resulting nutation amplitudes against realistic estimations. We show that even allowing for large discrepancies related to atmospheric forcing, the ranges of the possible changes in the FCN and FICN periods and damping factors are small.