I had something of the second situation happen almost after the fact, for a landlord client of mine. It turned out OK, thank goodness!
Wife saw with her agent, 3 kids. Agent says, wife separating from husband, wants to be closer to work. Everything checks out, sign lease. Then I get a call from my client that husband got in touch trying to get dimensions of living room.. My alarm bells start going off, I contact her agent and ask. He says he knows nothing about it. I say, we really cant comment on their family situation, but I need him on the application before we do anything further. They say they are royalty from an African country (dont want to name it) and are P'd off that I would want to run back ground checks. MOre alarm bells!!! I tell my clients, hold on everything until we sort this out. Eventually, I get the information, run checks, find a simple assault charge against the husband that the wife apparently did not know about, and it is one big mess. I check with the town police, that charge was dropped, I tell my clients everything seems OK, go ahead. They get the keys but dont turn utilities to their name, Royalty dont need utilities, right? A week and a hald into the tenancy, no electricity so garage door wont open, fridge is leaking puddles. Royalty doesnt want to deal with me because I am being tough on them, LOL!
Anyways, long story short, they have been model tenants since then, but you wouldnt know it from all the drama going in. I am happy for my clients:-) There is almost always more to a tenant's story, some good, mostly bad:-) Be patient, listen to your gut and apply criteria uniformly, you will be fine. It is slow at this time, so dont try and just fill the place. Better to have no deal than a bad deal! Good Luck..