Episode #1.1 - S1-E1
Factual error: This is set in 1933. When the killer comes back to his lodgings in episode 1, Lily on the stairs is humming "Somewhere over the rainbow", which was written for The Wizard of Oz in 1939. She also happens to wear bright red shoes, which feels like yet another Wizard of Oz reference. Interesting enough, the subtitles say that she is humming a different song, "Night and day" which she openly sings throughout the series and was already a hit in 1932. (00:44:10)