On the Past-o-Rama entrance sign, it says, "It's the boom!" This is a reference to the saying "It's the bomb." As with most of Past-o-Rama, it's probably wrong due to the limited knowledge of the 20th century they seem to have.
Past-o-Rama is a spoof of Futurama itself, and it has a caption of its own, "Located on the former side of Brooklyn".
In the Past-o-Rama commercial,  says, "Dy-no-mite!", a catchphrase of James "JJ" Evans, Jr. (Jimmy Walker) from Good Times.
In Past-o-Rama, a movie title called "Star Wars 9: Yoda's Bar Mitzvah" is seen, a reference to the Star Wars series.
The show in the beginning, "Cop Department," is a parody of Cops.