The pets presence can't hinder the enjoyment of others in the community "ie barking". 

Tell them you can't afford to replace the carpet throughout, you weren't aware the presence of a cat could be such a problem, and let them out of their lease without penalty.

If you believe there to be a presence of toxic mold in your home, you could perform an air quality test and duct swab and send it off to the lab at UF for testing.

Tenant does hereby release Landlord and Agent from any and all claims  or liability to Tenant, Tenant's authorized  occupants, or guests or invitees, and does hereby agree to indemnify and hold Landlord and Agent harmless, from and against any and all losses, damages, claims, suits, costs (including reasonable attorneys  fees and costs) or other  liabilities  whatsoever arising  from the presence of insects or pests in the Dwelling Unit, and/or resulting from Tenant's failure  to comply with the provisions  of this subsection or any other provisions of law."

His studio apartment was quite small and felt even smaller due to the ominous presence of a giant cross made out of heavy hand-hewn timbers, which he would haul around the courtyard and perimeter of the apartment complex nightly while wearing not much besides an actual crown of thorns, while drinking red wine and flagellating himself with a leather whip, reliving the blood sacrifice that redeemed us all as a way to thank Jesus for delivering him from the box of snakes (and freaking out the other residents in the apartment complex in the process, although weirdly they all just kind of ignored him). 

I would hope the seller has disclosed the presence of the mold to the tenants, but I would definitely ask him this.

. -- A receipt for a security deposit shall notify the tenant of the following: (1) The right to have the dwelling unit inspected by the landlord in the tenant's presence for the purpose of making a written list of damages that exist at the commencement of the tenancy if the tenant so requests by certified mail within 15 days of the tenant's occupancy; (2) The right to be present when the landlord inspects the premises at the end of the tenancy in order to determine if any damage was done to the premises if the tenant notifies the landlord by certified mail at least 15 days prior to the date of the tenant's intended move, of the tenant's intention to move, the date of moving, and the tenant's new address; (3) The landlord's obligation to conduct the inspection within 5 days before or after the tenant's stated date of intended moving; (4) The landlord's obligation to notify the tenant in writing of the date of the inspection; (5) The tenant's right to receive, by first-class mail, delivered to the last known address of the tenant, a written list of the charges against the security deposit claimed by the landlord and the actual costs, within 45 days after the termination of the tenancy; (6) The obligation of the landlord to return any unused portion of the security deposit, by first-class mail, addressed to the tenant's last known address within 45 days after the termination of the tenancy; and (7) A statement that failure of the landlord to comply with the security deposit law may result in the landlord being liable to the tenant for a penalty of up to 3 times the security deposit withheld, plus reasonable attorney's fees.

You prevent this by being proactive, don't rent to people with questionable passes, and make your presence known, if they think no one will ever come by, people will try and get away with stuff!

I intentionally steered clear of the big-name providers, you know, the ones with a massive online presence.

James Wise is active here has a big online presence.