On the nuclear side I think the danger is purely reputational damage towards the company behind the LLM.

If a journalist can prompt the LLM to tell them how to build a nuclear warhead. Even if the output text is nothing specific, or not even correct they can find an “expert” who will claim on the record that the description is plausible and at least directionally correct. Even if there is nothing in there a first year physics student wouldn’t already know. The journalist could then twist that story into a “company X’s LLM told us how to build a nuclear weapon”. It would be a PR disaster.

The real barriers to someone starting their own nuclear weapons program in their shed is not knowledge but materials. They won’t have the right kind and right quantity of fissile material. And if they try to acquire it they will stick out like a sore thumb. You can’t buy that stuff. And even just acquiring the refining capacity would be suss. It would ring all kind of alarm bells to the kind of inteligence agencies whose job is to monitor these things.

I’m a lot less certain about biological dangers. Setting up a lab where you can make dangerous biological materials require a lot less stuff. Therefore a lot more plausible that someone could hide their lab. There is also a lot more opportunity to disguise such a lab as something legitimate. Therefore lack of know-how is more of a limiting factor there.