The oversized pack the Squires carry for the Knights is a joke at the games where carrying too many items can overencumber your character.
The series is set within the same continuity as the video game franchise but will be an original story. Executive producer Todd Howard said he wanted to avoid adapting the video games. To note, Todd Howard is not the original creator of the Fallout game series.
The town of "Filly" is called that because it is built upon a landfill. It has nothing to do with Philadelphia, PA.
Cooper Howard's fictional western film, "A Man and His Dog" is a reference to the Harlan Ellison short story "A Boy and His Dog", adapted as Apocalypse 2024 (1975). The post-apocalyptic story of a boy and his telepathic dog are a huge influence on the Fallout games, particularly the character of Dogmeat.
Despite Vault 33 existing in the same area the first two games are set, Vault 33 is never seen in those games. While some erroneously regard this as a plot hole of the show, one of the game designers from Fallout 1, Jesse Heinig, said this: "We didn't have a definitive list of Vaults during development of the original game, and the creation of new Vaults in southern California for the TV show 25ish years later is way outside of the scope of any of our planning... There are any number of reasons that the Master might not have any record of a Vault right under their noses, since there is no guarantee that the Master has access to an actual and complete listing of every Vault."