Song of the Younger World - S2-E20
Factual error: The 19th Century reformatory has modern electric light bulbs hanging from the corridor ceilings. (00:21:10)
Sucker Bait - S1-E7
Factual error: It is quite true that atoms that do not occur naturally are bad for humans. However, in a space age as this story's, that would apply to most or even all planets. It would be a well known risk that didn't require an abnormal specialist to diagnose. (This fact rarely figures in other SF, because it would severely limit most stories).
Factual error: The FBI agent introduces himself and says "Mike Weston - I did my thesis on Joe Carol at the academy." FBI agents are required to have a university degree, but they don't write thesis' at the academy. A person is either in a university or at Quantico getting trained. They are not writing papers at Quantico. They need the degree beforehand to get in. (00:10:30 - 00:11:30)
Factual error: Constantine's driving licence is shown - it's a UK licence, but no. 7 where his signature should be is blank, and no. 8 where his full address should be simply says "England, United Kingdom." Both are printed onto the licence when it's issued - without that info it would never be issued in the first place. And it's not a fake, because why would he have a fake licence with his real information on it? It's just an incomplete prop.