Correctness can just mean "does what it's intended to do". This is fairly unambiguous in cases such as if you intend to implement A* Search. If you hit a NPE and your program explodes, or if you aren't calling your heuristic (central to A*), then you have skimped on correctness. Furthermore, basically any time you hit something like a runtime error you likely did not intend to hit it. Therefore, regardless of problem domain, taking approaches that minimize these types of errors is an uncontroversial way that correctness can be prioritized.

People don't even think consistently, so correctness is an ever-moving target (aka a negotiation).

Case in point: from reading discussions about the C standard, my impression is that a compliant compiler is "correct" if it reads your program that dereferences a null pointer and blows up the world.

If a null pointer handler in a nuclear warhead firmware caused immediate detonation, that would certainly be correct according to C standard ;).