Out of Time - S2-E1
Other mistake: Sara tells Jefferson that the professor has a one hell of a right hook (referring to Martin knocking Einstein out). Jefferson replies, "seriously, Gray punched him out?" The subtitles mistakenly say "Ray."
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.
Factual error: The astronaut in 1970 says "run any test you like I just want to be on that shuttle". The shuttle wasn't in operation until 1981, the mission he's referring to is the Apollo 13 rocket. (00:39:50)
Factual error: When Ray is on the moon, he's getting the spear from the flag that was planted in the Sea of Tranquility, from the Apollo 11 mission. When we see the flag, it's still standing up. However, Buzz Aldrin saw, and reported, that the flag fell over from the rocket's exhaust as they left the moon, and no one from Apollo 12 put it back up.