Each state has different "landlord/tenant" laws, but here in Michigan, there is no law that says landlords are required to change carpet and repaint every so often. Landlords are required to provide a safe dwelling for the tenant. Cosmetic items will not likely fall under this category, but you definitely have the right to request any sort of repairs. When you say no rental agreement, do you mean you are on a month to month lease? Have you made communication to your landlord that you want these repairs done? I would suggest putting your requests in writing at first. If you don't get a response, I would contact an attorney and suggest putting your rent in an escrow account with the courts. I am not an attorney, but I have 10 years of property management experience. Good luck to you :-)
Most Realtors do rentals in addition to working with buyers and sellers. What area are you looking for a rental in?