Big Bird wore the same tie in China.
Prince Sahu tells Big Bird that he is 4306 (and a half) years old, which would mean he was born in 2322 BCE during the Sixth Dynasty. The Sixth Dynasty is often referred to as the last dynasty of the Old Kingdom.
The Caroline Kennedy listed in the Don't Eat the Pictures credits as a coordinating producer is the same Caroline Kennedy who is the daughter of President John F. Kennedy and Jacqueline Bouvier Kennedy Onassis. After graduating from Harvard University and before entering Columbia Law School, Caroline Kennedy worked as a research assistant in the film and TV department at the Metropolitan Museum of Art, and as such served as a coordinating liaison between the museum and the producers of Don't Eat the Pictures. While Kennedy worked for the Met, she received some letters from a disturbed man who threatened to kill her by bombing the museum; one of the Met employees she turned to for help during that situation, exhibits designer Edwin Schlossberg, became her husband in 1986.
Prince Sahu tells Big Bird and Snuffy that he likes to go to Queen Hatshepsut or the Temple of Dendur when he needs to think. Sahu, who was born during the 6th dynasty (around 2300 BCE), would not have heard of Hatshepsut or the temple when he was living in Egypt. Queen Hatshepsut was born 900 years after Sahu and the Temple of Dendur was built more than 2000 years after the young prince was born.
The television special was taped in July and August 1983, in which it was coincided with The Muppets Take Manhattan.