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.
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.
Continuity mistake: The girl being rescued at the beginning goes from standing close to the wall, looking blank in one shot, to being further away from it looking concerned in the next.
Smile Time - S5-E14
Continuity mistake: Angel is coming down the hall in the Smile Time set and he sees the trash man walking past him. In the behind shot, Angel is farther back, but when it shows the side and front shot, he's right behind him.
Answer: Everybody including Angel saw her. After helping them and then being left alone to talk to Angel, Cordelia says that the Powers That Be let her come back one more time to help them. After Angel gets a call saying that she died, he realises that it was her spirit that was helping them the entire time.