Prospective tenants in a rush to move: what to look out for?

[Account Closed]

I have a prospective tenant that is eager to move b/c he is living out of a hotel now (in the midst of a divorce; divorce hasn't finalized yet).

He hasn't started the application process yet but when I mentioned cost to move in + presenting 2 pay stubs and 2 bank statements, he didn't seem to wince (though, we were speaking over the phone).

His income, credit score, criminal history, eviction history still hasn't been verified/checked.

But I'm still new to this and I don't know if tenants in a rush to move can cause problems later... In your experience, can they?