The "Invasion Schedule" that Sokka has is actually a standard schedule for animation deadlines, such as those used on the show.
The fishing town built on top of the water is similar to towns found in southeast Asia.
The hat Katara wears may be based on the Chinese weimao. The weimao was a wide-brim hat with a veil. They were used to hide the face as it was traditional for Chinese women to conceal their bodies; as this tradition faded, the need to conceal the face prevailed.
This episode features Katara with a secret persona, which is similar to Zuko's secret persona, the Blue Spirit. Many online fans have "shipped" Katara and Zuko due to this similarity among other parallels.