This is definitely the most interesting question in a ton of AI applications. I think folks should be really be spending a lot of time on figuring out how to deterministically check AI outputs in a way that's reliable in order to reduce the amount of work a human has to check, and to build tools that speed up the checking process.
Thinking about all of the fake citations in legal submissions that have come up of late, it seems pretty straightforward to set up a regex that captures all forms in which a cited case might be written (I could be wrong but I'd assume there's some standard variety of formats) and search those against a database (again assuming such a database exists) to ensure they all exist.
Then for the tougher problem of making sure that the cited cases say whatever the document citing them says they do, you could have an LLM run through the document, pull out the text with the case name and text about why it's being cited, then read the case and try to determine whether the reason for citing it is valid. Rather than just give a yes/no, you'd put the doc in front of the user and let them jump from citation to citation. On each citation, it'd pop up a card that shows the literal text of why it's being cited, a judgement from the LLM of whether it matches what the case says, and snippets of text from the case as evidence + deeplinks to that text within the case.
Or maybe you wouldn't even want to give the LLM's judgement since people might rely on that without reading, but there's definitely a way to speed up the review.
I believe OpenEvidence does something like this with medical papers. If you ask it a medical question, it doesn't answer so much as link you directly to the relevant papers so you can read them and determine if they're useful. Avoids all of the potential risks of using an LLM but still hugely valuable and time-saving for docs.