For example, they could have really bad credit and a lot of debt, or their family members could have been in jail for various crimes in the past. Perhaps they themselves have a criminal record too.

I don't think any of these things necessarily mean you're being catfished or that the other person is a bad person. People making foolish credit decisions in their youth is extremely common, and given the freewheeling police culture and "lock 'em up and throw away the key" attitude of much of American society, I'd imagine your odds finding someone who has no family members who have ever had legal trouble is probably less than half-half.

If you find these things out and confront your companion about them and they deny them or act cagey, that might be a red flag, whereas acknowledging them may be a sign of maturity. On the other hand, they may also be offended that you've been digging into their and their family's past like that, and I don't think that's an unreasonable reaction, especially early into a relationship.