While landlords to have to abide by applicable health, building and safety codes and keep the apartment in a "fit and habitable condition," there is no Ohio law that makes a landlord replace carpet or repaint walls.
If you think you're paying too much in rent, explain this to your landlord. Ask him/her to replace carpet and repaint walls. If your landlord refuses, move out.
Disclaimer: This does not constitute legal advice. No attorney-client relationship has been formed through this answer.