The University of Florida's student legal services site suggests that cleaning costs can be deducted:
Quote Quoting What Steps Can I Take to Protect My Security Deposit?
When you take occupancy of the apartment, complete a thorough written inventory of the apartment's condition and have the landlord or an impartial witness sign the inventory. Make sure you keep a copy of the inventory. This helps protect you from the landlords claiming you caused pre-existing damage. When you move out, completely and thoroughly clean the apartment. Some landlords provide a checklist outlining the cleaning they expect you to do. Keep all receipts for cleaning supplies and steam-cleaner rentals as evidence. Before you leave, ask the landlord to inspect the premises with you. Complete a move-out ckecklist and make sure the landlord signs and dates it. Use an impartial witness if the landlord is not available or refuses your request. Move-in and move-out photographs or videotape are also strongly recommended in case there is a dispute.
I don't think the cost of certified mail is a reasonable charge and, accepting your claim, don't think the carpet replacement cost could be justified (and even if it could, you should only pay a depreciated amount and not the full replacement cost).


Your remedy? Small claims court.