The one thing that popped out at me is : be sure you have rental Property liability insurance - i would not be surprised if these tenants start threatening legal action for injuries caused by an unsafe dwelling. 

We doubt that  he sustained any injury on our property, he claimed that he was having surgery on his leg about 2 weeks before he sustained the injury, he may  even have moved out before the date of the injury. 

I spent six years as a litigator defending property owners from personal injury claims. 

This may be a stopgap measure but I have news - laws vary from one jurisdiction to another but in general tenants are straw men, they have little to no assets, while injury lawyers see landlords as owners of property that is worth going after in court.

.- - - - - - - - - -PET AGREEMENT  (Addendum to Rental Agreement)The Month-To-Month Rental Agreement (the “Agreement”) dated_______________________ between __________________________________________________________________________, as Landlord and ________________________________________________________________________, as Tenant of real property located at _______________________________________________________, is hereby amended to include the following terms and conditions: The rental agreement specifically prohibits keeping pets and animals without Landlord permission; Tenant agrees to follow these terms and conditions in exchange for permission to keep a specific pet:Condition for keeping a pet:Tenant agrees to pay additional rent of _____________ per month for the privilege of keeping this pet.Tenant agrees to pay additional security deposit of ______________ for the privilege of keeping this pet.Name of pet: __________________________Description of pet: _______________________ (type, breed, color, age)Veterinarian: __________________________Emergency Caretaker: ____________________Tenant agrees to:1.Provide proper care for the pet in accordance with veterinary recommendations or ASPCA (American Society for the Prevention of Cruelty to Animals) guidelines.See www.aspca.org.2.Adhere to local ordinances, including leash, vaccination, and tag/licensing, requirements.3.Clean up after the pet and dispose of pet waste properly and quickly.4.Not to leave pet food or water outside the dwelling, as it could attract other animals.5.Not to leave the pet unattended for any unreasonable periods of time.6.Keep the pet from being noisy, aggressive, or from causing any annoyance or discomfort to others.7.Immediately remedy any complaints that arise from pet behavior.8.Immediately pay for any damage, loss, or expense caused to others by the pet.9.Provide pet with regular health care, to include inoculations as recommended by a veterinarian.10.Spay or neuter the pet when it becomes of age to do so.11.Arrange for an emergency caretaker for the pet.Tenant agrees to indemnify, hold harmless and defend Landlord against all liability, judgments, expenses (including attorney fees), or claims by third parties for any injury to any person or damage to property caused by Tenant’s pet.Landlord reserves the right to revoke permission to keep the pet should Tenant break this agreement or provide false or misleading information.

.; also he wants me to live in and take care of the property due to a work a injury that's recently placed me on temporary disability from the federal government..

Government operates the same way.The maliciously bad landlords (criminals, for all intents and purposes) will ignore the law, figure out how to fudge the paperwork, or avoid detection so it won't do anything to prevent a fire or accident or injury in their properties because the city doesn't have the manpower to go out and enforce it without a complaint.But hey, in the meantime it'll make nanny state bureaucrats feel like they're doing good deeds and fill the city's coffers off the backs of the good landlords at little or no cost to the city, so of course they'll figure out how to push this thing through.

Do you think the written contract should include something about injury?

Keep in mind this is probably advice to follow the lemmings and you will almost certainly waste your time and money pursuing it, but this is what you need to do.First, and most important, consult a personal injury lawyer.  

Then, to add insult to injury, they depreciated the garage value saying it was old and took 25% off the lowest estimate!