I don't have a problem with more obvious failures. My problem is when the LLM makes a credible claim with its generated text that turns out to have some minor issue that catches me a month later. Generally I have to treat LLM responses as similar to a random comment I find on Reddit.
However, I'm really happy when an LLM provides sources that I can check. Best feature ever!
I have had an issue using Claude for research; it will often cite certain sources, and when I ask why the data it is using is not in the source it will apologize, do some more processing, and then realize that the claim is in a different source (or doesn't exist at all).
Still useful, but hopefully this gets ironed out in the future so I don't have to spend so much time vetting every claim and its associated source.
However, I'm really happy when an LLM provides sources that I can check. Best feature ever!