Factual error: At the beginning of the episode, when Snart stole the female soldier's keycard in 1986, she is wearing the U.S. Army's Combat Infantryman Badge (CIB), a combat award for infantry and Special Forces soldiers. It is not possible for a woman to have a CIB in 1986 because infantry and Special Forces were closed to women at the time.
Continuity mistake: While all the heroes are in front of the aliens ready to fight, the sun on the floor changes between shots.
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.
Suggested correction: The term "Illegal drinking" is actually in reference to people going to locations that were selling alcohol illegally to drink it, hence it is illegal drinking.
That still would not be illegal drinking.