Factual error: The address on Lee's business card shows her zip code for Atlanta, GA as "11453." This is a non-existent US zip code, and the zip code for Atlanta is "303xx."
Episode One - S1-E1
Factual error: In the fairground chase the characters jump over some Heras fencing that wasn't invented until the next decade.
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.