In the steam room, Cliff talks about crawling out from the wreckage of his life. In the comics, "Crawling From the Wreckage" was the title of Grant Morrison's first story arc on the Doom Patrol book, which the series is largely based on.
When Cliff joins Kay and Rita on the dance floor, he busts some moves from "Blast From the Past"(1999), which starred Brendan Frasier.
The music played on the old gramophone is Siegfried's funeral march from Wagner's opera Gotterdammerung (Twilight of the Gods).