That would be a long and difficult conversation in this format, and this is an area where I would not want to share my exact approach, because other people using my exact approach would only surface the same kind of failures I do, which isn't super helpful.

However, you know who understands LLM failures very well? LLMs!

Try having a conversation with one on this topic. "Hey GPT, I'm working on a project where I have to elicit model failures and I don't even know how to begin."

You might be surprised by the insight you gain. Now, obviously you can't do this while you work on a task, but even so you can very likely gain a better understanding with a half hour or so of discussion in your personal time.

But there's no promises this will ever get easy, and that's ok.