Many of the sight gags here were related to popular radio and film stars of the era. Although they may seem dated now, audiences of the era would have recognized them and laughed at the parody.
This cartoon was released less than two months before the US entered WW2. Both nylon (introduced in 1938) and silk, used for ladies' hosiery, would become rationed materials, as they were used to construct parachutes for the war effort.
Wasp waisted fashions have been popular over through the centuries, usually through the use of corsetry, as shown here.
The slow horsefly says, "I've been hanging around Bing Crosby's horses too long!" Crosby was well known as a horse breeder whose horses very seldom finished in the money.