In the Episode "Apostles" as Azmaria pumps water, we see that here hair is tied back. But when we see her again after hearing disturbing news, her hair is loose.
At the end of "Apostles" Rosett does not have her veil on. But when we see her again in the next episode, she has it on. There is no reason why they would put it back on her if she was unconscious.
At the beginning of episode 6, the location text which tells us this takes place in South Brooklyn NY reads, "Broklym" instead. Brooklyn is misspelled several times in subtitles.
In episode four, during the close-up of the newspaper regarding Recardo, the small text itself has nothing to do with the topic of the paper. It is current news, not of the 1920s.
Rosette and Chrono go on a mission in a casino on the Las Vegas Strip, but the first casino on the Strip wasn't built until 1931, several years after the story is set.