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.
A New World - S3-E20
Revealing mistake: When Connor runs out of the hotel and Groo and Gunn drag Angel out of the sunlight, Angel's reflection can be seen in the door behind him just as Cordelia steps outside. Angel is a vampire: he should not cast any reflection.
Benediction - S3-E21
Audio problem: When Cordelia has her vision about the vampires at the bar, her lips don't match the words "Vampires, a gang of them".
Continuity mistake: The entire area around Cordelia and Skip is supposed to be frozen in time. However, there is a car driving freely across a bridge in the background behind Cordelia. (The background is blurred, so it is difficult to see.)