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.
A New World - S3-E20
Revealing mistake: The Axe that Groo throws at Conner at the start of the episode (Obviously CGI) doesn't match the movements of his hand, it leaves his hand before he actually throws it. (00:01:40)
A New World - S3-E20
Revealing mistake: The first stake that Conner fires from his stake cannon (Obviously CGI) doesn't seem to emerge properly from the barrel of the cannon, it emerges out of thin air from the side. (00:01:25)