I fly about 900 hours a year with the GPS being the primary navigation tool and have only seen two GPS failures in the last ten years.
The GPS flagged the failure both times.
I have had no "incorrect" position problems if this had happend it would have been picked up by the other inputs to the FMS system (2x IRS 2x VOR 5x DME).
The results in the "big" aircraft are reflected by the performance in my light aircraft with an IFR approved GPS fitted, in my opinion most of the problems are with non-approved systemes and I would guess that poor aeriel position and getting tangled in the yards of wire that conect these things to the cigar lighter socket are the most lightley reasons for faiure. . . . . not the actual GPS unit!
I have flown a few of the UK CAA GPS trial approaches in my light aircraft and it all went very well, the sooner that ADF approaches are replaced by GPS the better.