On normal Radeons at stock clocks and voltages, and are not overheating, have a known error rate (which is something like 1 error per several hundred million instructions)
One error per several hundred million instructions... where are you getting that information from? (an honest question, I'd like to learn more)
A 58xx series, from information I can find, can do between one and four instructions per clock. If it is clocked at 775000000 cycles per second (775 MHz), that's up to 3.1 billion instructions per second. So according to your information there would be many errors per second.
I think I meant 1 per several hundred billion. Its in the chip specification somewhere, ask AMD.
a silicon chip is not supposed to have errors, and will only occur if: incorrect voltage, incorrect temperature range, the silicon chip itself is faulty, something extremely rare such as a cosmic ray bouncing off and [in the case of RAM] 'flipping a bit' perhaps once every few weeks
Bzzt, wrong. GPU hardware does not use the same manufacturing process CPU hardware typically does. GPUs are not mission critical hardware, and rare calculation errors are considered acceptable.
You are correct about "incorrect" voltage, however you assume that it is incorrect at all. The professional versions of these cards run at lower clock rates and lower voltages to reduce the error rate. Consumer cards are not ran at incorrect settings, they are merely ran at settings that lead to acceptable levels of errors.