YOU sue the SELLER.So now look for CONTRACT defenses by the seller.

@Kayla Truong As a criminal defense attorney I would never rent to anyone with a domestic violence history.  

http://www.ahs.com/homeowners/plans-costs/plans-costs.htmlAn AHS Home Warranty is a homeowner’s best defense against expensive repair and replacement bills.An American Home Shield Home Warranty is a service contract that covers the repair or replacement of many of the most frequently occurring breakdowns of certain home system components and appliances.

You aren't legally obligated to give any information about your tenants.If New Landlord relies to his or her detriment on assurances from Old Landlord that there was nothing to worry about regarding a tenant, then New Landlord could sue Old Landlord for her/his losses.Depending on your jurisdiction, you could be held liable for slander or libel by a tenant, but in almost all jurisdictions, truth is a perfect defense. 

But, really, your best defense as far as any problems, is the initial screening.  

Put them on the defense.  

Then, they'd usually want a request via fax on letterhead, which I did not have, as a resident manager working for an old fashioned owner.Other than using other good sleuthing techniques and credit, criminal, eviction, employment checks - your next best defense is a month to month agreement.And remember that you can deny them for nearly anything you can think of.  

Does the argument against doing this of "Their dog should have had rabies shots" sound like a reasonable defense for not getting rid of the wild animals?

You won't learn anything if you are so defensive, regardless if the mode of information is less than you'd prefer.The fact that you are even asking if you should rent to any of these applicants shows that you don't know what you're doing. 

For example, I used home warranties as my first line of 'defense' against maintenance issues.