When the announcer introduces the judges, Senator and Mrs. Clatterbuck, Mrs. Clatterbuck's hair is parted down the middle and feathered under her pillbox hat. A minute later, in the same scene, she's wearing the same hat but her hair is just combed back with no part and is not feathered.
When the girls first arrive in Myrtle Beach, they drive by an amusement park in which a steel looping roller coaster is clearly visible. The first modern coaster with a loop wasn't introduced until 1976.
When the girls are first driving through the beach party, a modern-day Coke machine is visible in the background.
The maroon Cadillac DeVille convertible that the girls drive to Myrtle Beach is a 1964 model, and since new models traditionally did not appear until September of the year before (9/63 for a 1964 model) it should not appear in a movie set in June (right after HS graduation) 1963. You can tell it's a 1964 model by the maroon (body colored) band across the center of the grille.
The Furuno radar unit on top of Senator Clatterbuck's yacht is too modern for 1963.