Both tenants have been problematic and there are frequent unsavory visitors to the property and I get reports from the neighbors that they're noisy and there's a lot of foot traffic.

They may not have room for visitors but just serious buyers.  

For example, if a tenants dog bites a visitor and that visitor sues both him and you (or just you) the tenants liability insurance will provide defense for both you and pay settlements up to his limits. 

She had many late night male visitors to her place and one forced entry into her apartment which damaged the front door.

Typically most leases allow visitors to stay 15 days, otherwise tenants are in violation of the lease agreement.  

And I swear that our bully has detered potential "visitors" to our house. 

For that reason, I point out to tenants that they are responsible for damage caused to the property, regardless if they did it, their visitor did it or the SWAT team does it.

Airbnb guest is a foreign visitor, and wants to pay directly to save on all their airbnb fees.

Then when the tenants mother died, she had visitors coming when her mother was on her death bed.

Oh, will your insurance pay should a visitor get bitten by that dog!!!