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.
Heads Of Beef / Klub Katz - S1-E11
Factual error: In "Klub Katz" the captian yells "Iceburg, Iceburg, on the starboard side." But when you see the iceburg and the ship, the iceburg was about to hit the bow of the ship.
Factual error: When Nasedo kidnaps Liz, he stops in a gas station to leave the FBI another clue. As he is pulling into the station, the sign above the gas pumps misspells the word "brakes" as "breaks."