At what point in a relationship is it appropriate to reveal non-apparent flaws?

Let me ask this both generally and specifically. Suppose there’s something about you that some people might consider a negative quality, like a predisposition to a serious genetic disease, a criminal record from long ago, or financial problems.

Someone who was just getting to you know you would have no way of finding these things out unless you told him/her. So at what point is it appropriate to reveal them?

I ask because, more specifically, I find myself feeling sort of embarrassed about my financial situation. I am dating someone new who is a couple years older but leaps and bounds more financially secure than I am. I have a huge amount of debt from college and, perhaps foolishly, when I had a job I spent all my available money paying off that debt rather than saving. I took a pay cut of more than 50% to go back to school, so now I make just enough to get by. Each time I manage to save even a little, it seems like some catastrophe shows up (e.g. death in the family). So I am in a position where I usually can’t even offer to pick up the check when we go out to dinner, and he is a responsible grownup who has alluded to having a good deal of money saved.

So have you ever been in a similar situation, in which you felt like you needed to disclose something but weren’t sure how or when to bring it up? What about the money thing? Have you had relationships that were wildly imbalanced, and if so, how did you manage it?