The issue has been litigated over and over again and I understand from my attorney that courts have never upheld the right of the landlord to charge tenants for cleaning, which is considered to be part of the ordinary wear and tear on the apartment. The student legal services at my university spent a whole season representing tenants against landlords over this issues because deducting cleaning expenses is such a common practice. The guide published by the legal aid society says the same thing.
You're paraphrasing
5321.05 pretty badly. Here's what it says, excerpting the relevant bits:
(A) A tenant who is a party to a rental agreement shall do all of the following:
(1) Keep that part of the premises that he occupies and uses safe and sanitary;
(2) Dispose of all rubbish, garbage, and other waste in a clean, safe, and sanitary manner;
(3) Keep all plumbing fixtures in the dwelling unit or used by him as clean as their condition permits;
(4) Use and operate all electrical and plumbing fixtures properly;
(5) Comply with the requirements imposed on tenants by all applicable state and local housing, health, and safety codes;
(6) Personally refrain and forbid any other person who is on the premises with his permission from intentionally or negligently destroying, defacing, damaging, or removing any fixture, appliance, or other part of the premises;
(7) Maintain in good working order and condition any range, refrigerator, washer, dryer, dishwasher, or other appliances supplied by the landlord and required to be maintained by the tenant under the terms and conditions of a written rental agreement;
The requirement is "safe and sanitary" only for the premises other than garbage and plumbing fixtures, which must also be clean. If there's dust on the floor in the corner of the room, the floor is still safe and sanitary; the tenant is not violating housing, health, or safety codes; and so the landlord can't take the fees for cleaning out of the security deposit.
(My last landlord was a scumbag piece of shit and tried to deduct for cleaning, and my attorney sent him a letter explaining this to him and he relented. He rents to hundreds of tenants and gets 10 or 15 of those letters every year, knowing he'll get away with charging the other 90% for it. I'm sure it wasn't an accident. I'm
not saying that all Ohio landlords who deduct for cleaning are beings of his moral caliber - he's just why I know this issue as it applies here forward and backward.)
ETA: Of course you should clean your place out when you move out. Our place was pristine and we could document it as such, which is why I wasn't about to accept $900 of cleaning fees. I'm moving out of my current house of three years later this week and it'll be spotless, because it's the right thing to do (and we'd like to have a positive reference, of course).
ETA2: You'll notice that 5321.04 has the same language for the landlord's responsibility with regards to a common area. If I live in an apartment building and spot dust in the corner of the hallway, and the landlord doesn't sweep it up, that's sure not grounds for me to start paying my rent into an escrow account.
(3) Keep all common areas of the premises in a safe and sanitary condition.