I have done that as well. Not a single time I asked an LLM for any sort of analysis that I could trust upon verification so I stopped doing that. If I need verify, much easier to just ask for suggestions of papers and books and do the analysis myself.

I guess this is subject matter dependent, certainly the LLM should be able to cite the papers/books for which it's deriving its critique. if it can't, then you know the advice it was giving is of poorer quality. I do that all the time

I guess there's a whole suite of skills that allow LLM use to be more or less useful. (I dont actually "guess" this, I sort of am pretty sure of it at this point, so it makes me wince when people call for total AI blackouts in education...would be better if they were part of an overall media literacy curriculum since people are going to be exposed to these things whether they think they're little infallible people, or complex systems with lots of caveats)

I always ask for sources. LLM analyses often fails by being simplistic or wrong in comparison with the sources it provides. More often than not, to the point that it is wasteful to ask it for analysis so I only ask for sources now and do my own analysis.