Character mistake: After Ray Palmer says he's an Eagle Scout, he says to Leonard Snart, "be helpful to others, scout's motto." The Boy Scout's motto (including Eagle Scouts) is "Be Prepared." "To help others at all times" is part of the Scout's oath, but that's different than its motto and not something an Eagle Scout would mix up.
Character mistake: When the Legends are talking about Chicago in the 20's, during prohibition, Nate says there was "illegal drinking." But prohibition didn't make drinking alcohol illegal. It was only the production, importation, transportation, or sale of alcohol that was illegal. As a historian, Nate would know this and not make that statement.