The suspicious movement the Inspector mentions is a blonde dancing ingenue who looks a bit like popular French actress Brigitte Bardot.
The laughing rooster butler sounds a bit like the animated Snoopy character in the first animated "Peanuts" cartoons.
The ring sized reel to reel tape recorder seen is a nod to the plethora of espionage films out at the time.
'Chicken Language Made Easy' is written by Dr. Cluck.
Eggs were commonly inspected for quality by shining a light behind them, as seen here with the candle used by Deux Deux.