Is there any elder law that prohibits the operation of an unsanitary nursing care home?

All nursing homes are subject to strict federal and state regulations. The Centers for Medicare and Medicaid Services (CMS) is a federal agency within the United States Department of Health and Human Services (DHHS) that administers the Medicare program and works in partnership with state governments to administer Medicaid, the State Children's Health Insurance Program (SCHIP), and health insurance portability standards. CMS also has other responsibilities, including the administrative simplification standards from the Health Insurance Portability and Accountability Act of 1996 (HIPAA) and quality standards in long-term care facilities (more commonly referred to as nursing homes) through its survey and certification process.
If you think that your grandmother's elder care home may not be in accordance to elder care law, you may contact the CMS or your local state authorities. In addition, it may benefit you to consult with an elder care attorney to determine the best course of action for your case.