We show how inferences of the solar internal rotation rate depend on different aspects of the mode fitting procedure. We study the stability of the rotation rate and its variation with time through inversions of frequency splittings data sets computed from fitting 364, 728 and 2088-day long Michelson Doppler Imager (MDI) time series, 72-day long MDI time series and 108-day long Global Oscillation Network Group (GONG) time series with different fitting methodologies and acquired during Cycle 23. The frequency splittings obtained from MDI and GONG time-series through different fitting techniques are inverted to analyze the effect of the fitting methodology on the inferred rotation rate. In particular, we present inversions based on either individual frequencies (as derived by the fitting technique developed by Korzennik 2005), or frequency splittings parametrized in terms of Clebsh-Gordon (CG) coefficients. We present the impact of using either individual frequencies or CG coefficients on the inversion results.