In my previous existence the 737 FMC we used was the version from the stone age so it was quite often the case that the old bird would throw a wobbler on longish sectors and you would see big Map shifts so we always had to back up using conventional NAV ie Manual/Auto.
In my new shiny B733 we have a up-to-date version of the FMC and with the Required Nav Performance function it is obvious when the Radio or IRS updates are slow cos they get near the limits. However, even when operating down in the Canaries and to Funchal the worst I have ever seen is a displacement of 8NM which isnt bad considering the FMC is relying on IRS input only for nearly 2 hours !
BA consider the RNP figure to be good enough to constitute a NAV Fix check nowadays so must be reliable I suppose !