The portrait on Kyoshi Island reads "Avatar Kyoshi on this day split and created Kyoshi Island. May our people and culture be forever isolated from the tyranny of the world."
Sokka's (Jack De Sena) detective outfit is likely a reference to Sherlock Holmes: a hat with large flaps protruding from it, a magnifying glass of some kind, and finally his dragon "pipe" which actually, comically, blows bubbles instead of containing any tobacco.
The name of the Rough Rhinos comes from US president Theodore Roosevelt's Rough Riders, a calvary division from the Spanish-American War.
Aang is locked in a device called a pillory. The pillory design was used in European countries such as France and Portugal. The Chinese utilized a similar device called a cangue or tcha that locks the head into a device similar to a pillory, but the hands are usually not locked into the device with the head.
Sokka's hat is similar to the Chinese futou, first seen in The Fortuneteller. The Earth Kingdom is largely based on the Ming Qing dynasties in China, the futous shown in the show are always blue, meaning they are a Water Tribe garment.