First problem is turning engineers into accountability sinks. This was a problem before LLMs too, but now a much bigger and structural problem with democratization of the capacity to produce plausible looking dumb code. You will be forced to underwrite more and more of that, and expected to absorb the downsides.

The root cause is the second problem; short of formal verification you can never exhaustively prove that your code works. You can demonstrate and automate that demonstration for a sensible subset of inputs and states and hope for the state of the world approximately staying that way (spoiler: it won't). This is why 100% test coverage in most cases is something bad. This is why sensible is the key operative attitude, which LLM suck at right now.

The root cause of that one is the third problem; your job is to solve a business problem. If your code is not helping the business problem, it actually is not working in the literal sense of the work. It is an artifact that does a thing, but it is not doing work. And since you're downstream of all the self-contradicting, ever changing requirements in a biased framing of a chaotic world, you can never prove or demonstrate that your code solves a business problem and that is the end state.