For example, my ad will state whether we accept pets, that we want provide income around 3x the rent, and that every adult must pass a credit/criminal screening.

Worse case, someone gets hurt or killed and you could be held criminally liable as part of the conspiracy to commit the crime even though you didn't intend the result.  

Criminals go where crime is easier and where they can avoid attention.

I started reading the IRC and realized it was not contrived by the same type of minds that write criminal laws immediately! 

The prospect completed an application and checks the credit and income boxes but does have a mark on the criminal record.

There's a whole section in the course about trials, sequence of events of the trial, how to get evidence entered into the record, when and where and how to object to errors...everything that is relevant to any case, civil or criminal is in there.

But upon looking at court records this person has multiple driving violations and charges of criminal trespassing.

Then we also look at background checks, and criminal history, and request a prior rental reference.You should not charge for a pet that is considered a support or service animal.

You can use RentSpree and the tenants pay $49 for the regular or $79 with criminal background check.

It might be worth it to install some security cameras and signs saying the property is being monitored to deter criminals.