The forbidden area in Flatland is named "Area 33H". "33" in hexadecimal ("H") is "51" in the decimal system, making this a sly reference to Area 51.
Real life brothers Martin Sheen and Joe Estevez play the 2-dimensional Brothers Square, Arthur and Abbott.
Hex's line "A still tongue makes a happy life" is a reference to a poster seen in the cult TV show The Prisoner (1967). Screenwriter Dano Johnson is a huge fan of the series and felt the oppressive Circle Priests would use similar language as the mysterious Village to subdue their citizens.
When the 2 dimensional characters turn to face different directions, animator Dano Johnson was forced to animate their lips and expressions upside down for extended periods of time.
Director Jeffrey Travis has a cameo as a yellow Circle Priest, while Director/Animator Dano Johnson plays multiple triangle guards.