Factual error: Spike suggests that Illyria and Drogyn play Crash Bandicoot. They appear to be playing on an original Xbox console. The episode was broadcast on May 12th 2004, meaning that the only Crash Bandicoot game they could possibly be playing would be The Wrath of Cortex which came out on April 5th 2002 in North America because every other Crash Bandicoot game that came out before that was only on the Sony PlayStation (with the exception of Crash Nitro Cart, but they're not playing that one). Both Illyria and Drogyn appear to be playing the game. However, The Wrath of Cortex was a single-player only game. They're not playing Crash Twinsanity (available for the Xbox) either as that didn't come out in North America until October 1st 2004 and it too was a single-player only game.
Continuity mistake: When Gunn is talking to Wesley near the start of the episode, he mentions that he's tracked Lindsay down, and that he's been living under the name "Doyle", and holds out the lease of his apartment. There's a close-up of the lease a few seconds later, in which the name "Lindsay McDonald" can be seen.
Factual error: When the mysterious person hands Cinco the business card during the 50's flashback (in the restaurant where he is sitting waiting for business), it says "Wolfram & Hart, Attorney's at Law." Clearly, there should be no apostrophe in "Attorneys" in this context - not a mistake a professional law firm would make.
Continuity mistake: In the season 5 episode 'Destiny' we see that the first time Angelus meets William, he has already adopted a more cockney accent, but in an earlier episode of BtVS (Fool For Love) Angelus asks Spike "Since when do you talk like that", suggesting he changed his accent after they met.
Plot hole: After learning about the prophecy, the gang realise that Spike's headed off already, getting a head start. Angel grabs another car and heads after him, but why use a car? We find out in the first or second episode this series that he's got access to a helicopter, which he uses to get a long way ahead of some bad guys, and which would have saved a lot of hassle this time. Can't imagine Wolfram and Hart's pilots only work in the daytime.
Other mistake: Angel implies that Wesley told him the device will kill Illyria. But this Angel is from earlier in the timeline, as shown when he tries to tell Wes and Spike things they have just told their Angel. So Wes did not tell this Angel that the Mutari generator will kill Illyria. Angel should know nothing about it. (00:36:30)
Character mistake: While Gunn and Lorne are interrogating Framkin he sings a couple bars of a song "Courage and Pluck". However, though he has the ability to read people when they sing, and in fact in the very next episode knows that Fred is about to fall from just the words "you make me happy", Lorne doesn't read him.