See what they get worked up, scared or insecure about.

I think you can pick up clues as long as the conversation is honest.

I have two friends as examples, one of them is mentally very stable, the other is the exact opposite. I ask a lot of questions, sometimes it's even just me asking myself, making a mental note out loud. My stable friend always responds with coherent arguments, honest "I don't know"s, barely gets triggered by heated arguments and almost never talk more than needed or socially appropriate.

Another is almost the exact opposite. Confronted with information she doesn't know, she gets very defensive and answer in an indirect way, or directly says the exposing subtext.

"Do you know how this works?" "Of course, what am I, stupid?!" / "No, is this easy for you? Am I stupid?"

"Did you finish that?" "I was working on something else!" (telling me she's not lazy)

(She grew up in an abusive and highly demanding family, it has left remnants in almost every conversation we've had together.)

You can always tell a lot from knowing what kind of interaction a person had/has with his/her parents or significant others. Loving, distant, abusive, etc.