If something crazy happens and someone gets injured inside your condo or decides to trash the place, I wouldn't expect the HOA to cover that.

Or if anyone is injured on the property that would also be covered within the limits.

The liability would not cover the medical per se, the injured party would have to prove some fault/negligence on your part which happened to get them injured for the liability to kick in for medical.

If the Tenant's dog bites someone, the injured party will go after the Tenant and the Landlord.

Unfortunately not being liable does not help a landlord feel better if their tenants dog injures or kills a neighbours pet or child.Getting rid of the tenant eliminates all possible concerns.

Owning the property you take the neighbor complaints, the risk of alot of people who could make liability claims if they get injured and you have a tenant who doesn't live there and may or may not maintain the standards you want.

That should provide all the protection you need from a tennant sueing you type situation to one where you drive your car into a doctors car, or other high earning professional, and he sues you for a year lost wages since they got injured and cant work.

We eventually evicted them for non payment of rent but they sure made things difficult before we got them out of there.At one point they broke the basement steps & tried to work themselves into a payday with the husband claiming he injured his back when he fell on the broken steps.

Landlords who violate codes are frequently fined and are held on criminal charges when someone gets injured. 

Either way, most city's health codes require the landlord to address pests, then it is just a matter of if the tenant can be charged.Regarding the garage door sensors, this is a potential safety issue and needs to be fixed, so tenant isn't injured and sues you.