How often do false-positive results show up on hepatitis c tests?

Depends: About 25% of people who have positive hcv antibody tests will have negative hcv viral load (RNA) tests. This means they are not chronically infected. Most of the time, this is not a true "false positive" test, because the person spontaneously cleared the infection after true exposure. The antibody test indicates exposure and the hcv RNA test indicates active infection.