What's the ultimate form of accountability? Someone choosing a school. If they don't like it, students don't advance academically or if they simply don't like the dress code, people can vote with their feet and leave the school.
In addition to competing for the customer (student), charter schools are subject to all the same forms of accountability found in conventional public schools, such as the federal measure of Adequate Yearly Progress, CSAP and state accreditation. Charter schools have an additional accountability component in that they must renew their charter every 3-5 years. This is typically a higher-stakes review and a look back to see if the original charter is being implemented.
Most charter school operators believe in the philosophy of charter schools adhering to a higher level of accountability. Most welcome the examination of what they're doing because they are accomplishing their goals. Charter schools that are not educating students or accomplishing the specific goals outlined in their charter shouldn't be renewed.