It's 1963, and Adam Clayton Powell refers to Marilyn Monroe in the present tense twice ("I saw Marilyn Monroe singing at your birthday party," he says to JFK in one instance), but Marilyn has been dead for a year.
Malcolm X famously had red hair, but is shown with black hair.
The Micro-Mate syringe used by Elise when shooting up has a CE regulatory mark that was introduced in 1993 and could not have been available at the time represented in the series.