A year later I found out they were scammers, who did $15,000 damage to another landlords property.

The locks that I use also specify to use Alkaline because Lithium can damage the electronics in the lock. 

If the oil runs out and results in damage to the system, the tenant will pay for the repair.I also recommend you be clear about this in your written lease for future renters.If there are repeated violations, terminate their lease and start with a new renter.

The property has been vacant for awhile, and any searches I do brings me back to the damaged/vacant property and no additional info. 

As long as you don't argue with them or make them mad, you should not experience more than the usual brain damage of getting permits.

I would think a rabbit does less damage than a cat or small dog. 

The unit was completely dirty, damaged and looked like a fixer upper.

For example, if a family is displaced due to extensive water damage that will take a few months to repair, the insurance company will then look to find temporary housing for their customer/displaced family.

Maybe best to wait to see whether Berkeley's brain damaged voters pass anti homeowner ballot measures. 

If you win, they will have to pay the extra expense of the filing fees, etc, on top of what you say your damages are (which would be the cost to hire someone else to complete the job).