One poster has already mentioned Aeroperu 603
Aeroperú Flight 603 - Wikipedia, the free encyclopedia
Although incredibly unfortunate, there is a transcript of the CVR where the Captain is clearly struggling, with the only sense coming from the FO.
The Captain's persistent intention of getting the AP back on is frightening when you're only getting erroneous readings back.
While near-invaluable nowadays, aircraft 'intelligence' is never going to be 100% accurate... ever! That's what the boys up front are there for aren't they
As mentioned earlier there's a reliance on AP/AT/FMC among newer boys/girls, not necessarily with blame attributable to them, but basic understanding of concept seems to be overlooked.