What if a married couple have great backgrounds but their kid has a history of drug arrests? 

For example, you cannot deny an applicant housing based on criminal charges or arrests (only convictions), and the conviction must present a "demonstrable risk to the safety of your residents and/or your property" in order for you to legally deny them housing.  

I look at them and say "awh, come on guys, I'm Poo, but know what, arrest HER!"

Some investors flew in from Israel to find their properties were abandoned and unlivable.Eventually, Dov got arrested on a federal warrant and the judge took away his passport.

I’ve had 3 tenant applications from folks with major felony drug arrests that made the papers.

Yep call the cops     when I’m having trouble with someone  I leave the Sheetrock knife in my car last thing you want is to get arrested for assault with a weapon.

When I moved into my house on Liberty St just 3 years ago, the cops almost arrested me several times over the course of a month for "breaking into a vacant building."

Next time I just tell them “you don’t want me to have you arrested again do you” in Brooklyn that was a 3 day thing.

They put out a warrant for his arrest for fraud.

I faced a similar case where I accepted prepaid rent - and then had trouble (drugs, arrest) with the significant other of the tenant.