Nursing Home Improvement and Accountability Act of 2021 This bill establishes reporting, staffing, and other quality control requirements for Medicare skilled nursing facilities and Medicaid nursing facilities. For example, the bill requires facilities to have registered professional nurses available 24-7 and to provide infection control services overseen by infection preventionists at least 40 hours per week. It also establishes civil penalties for facilities that submit inaccurate reports relating to staffing data and prohibits facilities from entering into pre-dispute arbitration agreements. Additionally, the Centers for Medicare & Medicaid Services (CMS) must conduct additional quality control and oversight, including (1) auditing facility cost reports; (2) reviewing the quality and effectiveness of compliance surveys; and (3) establishing on-site educational programming for facilities that fail to meet applicable standards. The CMS must also establish minimum staff-to-resident ratios for nursing staff, as it determines appropriate. The bill also establishes a demonstration program to evaluate the impact of certain changes to facility design, staffing, and care coordination on the health outcomes of residents in skilled nursing facilities. Among other requirements, selected facilities must serve between 5 and 14 residents, offer private rooms, and have resident and family councils.