Is a memory error actually an exploit? If so then are the unwanted changes that occur with no deliberate action an example of the computer cracking itself?
I think there is a useful distinction between a fault/error and an exploit. A fault is a break from the "desired" or "expected" semantics of a system, while an exploit is an algorithm to predictably utilize a fault (or faults) to access unexpected behaviours in that system. I.e., a buffer overflow is a fault in a program (breaking the expectation that a buffer's contents will remain within a certain bound), while an exploit targeting that overflow will likely allow running arbitrary code in a program not designed to do so.
So, I'd put it, the memory error can be leveraged in an exploit.
Errors can be used as part or all of an exploit. Exploiting a system requires that ethereal value of "intent", and I don't think anyone would (currently) argue that computers can have intent. Without that intent, it's just an error.
Philosophical...