"The Four Hundred" was a term used to describe the social elite in New York City during the late 1800's. The term was coined by Ward McAllister, who was the self-described "arbiter of New York City high society" from the 1860's through the early 1890's. McAllister declared there was "only 400 people in fashionable New York Society who actually mattered and were of any importance." On February 16, 1892, McAllister named the official list of The Four Hundred in The New York Times.
When Lazlo looks down at the boys sleeping in the street, this is a nod to a picture by Danish-American photographer Jacob A. Riis, who famously documented the lives of the poor in late 19th century NYC in his photo series "How the Other Half Lives". Riis worked as a crime reporter for several decades and was close friends with Theodore Roosevelt. Riis is also a character in the book this show was inspired by.
The place azure blue color that Roosevelt's daughter, Alice, is wearing is called Alice Blue which was named after Alice Roosevelt. Alice Roosevelt frequently wore this color which was one of many reasons she was considered a fashion icon and American Princess.