If this were a hardware error, even a 1-in-a-trillion one, I would expect his machine to be unstable, locking up constantly, his file system growing errors on its own and constantly needing to be fsck'd/repaired/etc. Software errors can be responsible of errors that occur with literally any magnitude of frequency, from one in a zillion all the way to constantly.
Error correction technology is a slam dunk solution for these types of problems, but it has not yet been applied to all the systems that need it.
Luckily, in the context of bitcoin, this isn't so critical. There's redundancy everywhere, since there are hashes for everything, and a million other nodes checking your solution before it's accepted. The only real risk is getting your client dorked up, submitting what you think is a valid transaction and being confused when it's not accepted by the network. I don't think millions of dollars will be lost in Bitcoins due to this, but certainly, a client that can't recover from a bit error in the blockchain file could cause all sorts of problems for a high-volume user/company that would lose money from downtime.
I have never appreciated the value of ECC RAM, because I've done computation on computers for 10 years without ever noticing an explicit error. Although, I can see how certain applications need the guarantees against it. Regular RAM errors are measured in errors/day, whereas ECC RAM errors are measured in errors/century.