Often during scenes in the American Bandstand studio, what you see being filmed on the cameras does not always match what is happening on the stage (obviously because the cameras are showing clips of the original American Bandstand whereas the stage has actors attempting the recreate it).
In the pilot episode, which takes place in the fall of '63 (because subsequent episodes deal with the assassination of President Kennedy), the Beach Boys sing "Don't Worry Baby" on Bandstand. The song wasn't recorded until February 1964.
American Bandstand moved to California in February 1964.
In the series pilot episode, Jack refers to "Ara Parseghian and Notre Dame." The pilot is set in November of 1963 while Parseghian was hired by Notre Dame in December of that year.