Factual error: The Lockheed 1011 was only produced until 1984. There's no way that in 1999 Toby would be flying on one that "just came off the line 20 months ago."
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: Dr. Eve Russell seems to be a "jack of all trades" in the medical profession, but it's impossible for her to know everything about every medical condition. When Theresa is going to marry Ethan, she goes and gets birth control pills and takes her first pill the day before the wedding. That night they make love. The next day, the wedding never takes place and Theresa flies off to find Julian. She forgets her second pill and sleeps with Julian. Eve tells her that since she didn't take a pill before sleeping with Julian then the baby is his. Any doctor would know that (and also suggest that) birth control pills are not completely effective until a person has been taking them for at least seven days, and a secondary form of birth control should be used. There's no way that Theresa's just taking 1 pill would protect her from being pregnant by Ethan, and this would still warrant a paternity test.
Factual error: In the final scene where Grace Mayberry's house is raided in Trenton, NJ. a New Jersey State Trooper is wearing a badge on his chest. The NJSP has always worn a triangular shaped badge on their hats.
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."