Character mistake: When Faith arrives in LA she is carrying a bag. She puts it on the ground and then steals a man's jacket and wallet. Afterwards however, she leaves without picking up her bag.
Continuity mistake: When Faith is sitting at the window and looks at the piece of broken glass she used to torture Wesley, it has a different shape than the one she first takes to torture Wesley. When she drops it out the window it has its original shape again. (00:33:10)
Plot hole: During the scene where Angel tries to work out where Wesley is being held hostage we learn that the man Faith beat up at the start is still alive in the hospital and that it's his apartment she's staying in. Angel bursts into the apartment to save the day, but that's not possible without an invitation, as the owner is alive, whether or not he's actually there. (00:34:00 - 00:36:40)
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.