The MCDU is what we think the airplanes weighs, the FACs compute what the airplane thinks it weighs. Thus we have the stipulation to maintain increased minimum approach speeds with respect to VLS as computed by the FACs when operating in icing conditions (ice build up on unheated surfaces or worse ice building up on heated surfaces) In these cases the FACs can determine an increase in aircraft weight caused by ice buildup that the MCDU can not. (ACA - 457 incident - roll oscillations on landing led to this section of the FM)
Conversely improper functioning of the AOA vanes have caused at least one serious incident (LH-1829) and one haul loss (GXL-888T).
I believe the MCDU message "CHECK GROSS WEIGHT" should be a red flag to every Airbus pilot. If we see that message we have made either a serious error during FMGC programming, or we have a serious undetected (by us and the fuel system) fuel leak , or we have accumulated a tremendous amount of ice or we have a serious problem with our AOA system.