Landlords that are blatantly violating the law (slumlords, sexual harassment, violence, etc.). 

Credit, criminal, sexual offender list.  

This is the DE wording in 4603(b)(3), the Delaware Fair Housing Act: (3) To make, print or publish, or cause to be made, printed or published any notice, statement or advertisement, with respect to the sale or rental of a dwelling that indicates any preference, limitation or discrimination based on race, color, national origin, religion, creed, sex, marital status, familial status, source of income, age, sexual orientation, gender identity or disability, or an intention to make any such preference, limitation or discrimination.

I'm curious about screening for applicants who are registered sexual offenders.

In Redding, CA the drug addicts shooting up heroin in the parks was so bad rather than arrest them, they removed the playground equipment, and the public libraries in many towns are overrun with sexual predators using the computers.

Aside from engaging in assault, sexual assualt, or openingly engaging in some illegal activities.

@Steven Lowe and sure enough, the insults came flying - name calling, attacking my character, coming after me for my race, gender and sexuality, wishing harm to my family and myself - you name it, I think I've heard it in the last few days. 

I didn't have sexual relations with this woman, Miss Lewinsky...

The district attorney, Alvin Bragg, told prosecutors in his office in a memo that they should ask judges for jail or prison time only for the most serious offenses — including murder, sexual assault and economic crimes involving vast sums of money.And this ladies and gentlemen is called turning the asylum over to the inmates.

However when one states that folks with a record of a violent or sexual nature its pretty easy to say that is protecting people.