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.
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.