It's not your duty to do seasonal bird poop patrol.You can't be sued by her successfully for negligence, because why on earth would it be your legal duty to be sure no birds ever sit in the tree above her space and let loose?

Something else to consider in MFH...what happens when one tenant's negligence causes damage to another tenant's unit?

Any landlord that does is irresponsible and negligent in the operation of their business.

(2) Landlord will NOT pay to repair the following items unless caused by Landlord’s negligence: (a) conditions caused by Tenant, an Occupant, or any guest or invitee of Tenant; (b) damage to doors, windows, and screens; (c) damage from windows or doors left open; (d) damage from wastewater stoppages caused by foreign or improper objects in lines that exclusively serve the Property;I assume the toilet was working fine when the tenants moved in and at the stoppage is just located in the toilet, then this is something that was caused by the tenant or a guest and at the tenants responsibility.The only time we would charge an owner for clog is if the sewer line is collapsed and is usually evident by roots or mud in the line.If the sewer line is fine and any clogs are deemed the tenants responsibility.

But if the lawsuit was caused fully by their negligence, your policy would not cover them.  

If you do not take reasonable steps to protect yourself by protecting your tenants, you can be held liable for negligence. 

Landlords get fined and rent-escrowed by the state, and if they've been really negligent they get prosecuted, but generally they don't go to jail.Go to BREIA landlord meetings the last Monday of each month.

If the old couple fall due to uneven floor and sue me for negligence, would my homeowner insurance pay for that?

We fired one of our property managers a few weeks ago and are now hearing about issues of negligence and possible criminal activity with missing tenant payments and/or not properly handling security deposits.  

Yes, a tenant may be responsible for the actions of their guests, but only for those foreseeable actions they have a duty to prevent, and were negligent in the supervision there-of.