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)
Plot hole: When Angel is being pursued by the Lilliad demons, he is holding his son Connor and is talking to him in the car. Later on it is revealed that he is in fact holding a teddy bear with a bomb attached to it. If it wasn't his son, why was he talking to it? It couldn't be to fool the Lilliad demons because they wouldn't be able to hear him, as they were in separate vehicles.
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.
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.