Are you referencing Anything Goes or a different musical? "A glimpse of stocking was looked on as something shocking" refers to the stereotype of the 19th century where seeing a part of a ladies leg (always in stockings) was supposedly scandalous. Note that stockings were relatively opaque until the 20th century. You really don't see them being much of a moral issue until the 1920s when some women chose to wear shorter skirts and roll them down to expose bare knees.