A New World - S3-E20
Factual error: Connor has been raised since he was a few months old by Holtz, a man with a British accent, in a dimension where there are no other humans. There is no possible way he could have an American accent, yet from the moment of his return he speaks with one.
Suggested correction: The demons in Pylea spoke English with American accents (possibly due to Wolfram and Hart's interference), and in tie-in comics, demons in the dimension Connor and Holtz went to were shown speaking regular English, though these comics were released years later.
Factual error: The scenery is set in Berlin, following the 1989 Re-Union of Germany. Only thing is: the guards at the archive building use AK-47s, while after the Re-Union, the East German National People's Army and the West German Bundeswehr (Federal Defense Force) were joined - and the West Germans don't use any AKs.