To repeat and repeat ad nauseam. Vinyl records, as those readers who remember them will recall, have spiraling grooves in which the photograph needle picked up the sound. When a groove developed a crack or other imperfection, the needle became stuck and the sound kept repeating until someone moved the phonograph arm to the next groove. The expression was applied to anyone who repeated a remark or request over and over until it sounded like a broken record . . . a broken record . . . a broken record.