Revealing mistake: In the last scene of the episode, Angel kicks the guy out of the glass building. This guy's a vampire, and you can see his reflection in the glass windows. Vampires aren't supposed to have reflections.
Revealing mistake: In the scene when Angel, a vampire, runs after the barman towards the end, after the barman has tried to pass on the demon to Kate and Angel stopped him, there is a mirror, and when Angel runs past it, he has a reflection. (00:38:20)
Revealing mistake: In the scene where Kate finds her father dead, just after the shot of his neck wounds, she is sitting over him and you can see the father blinking a few times. (00:33:00)
Revealing mistake: When Angel stands at the cabinet with a file folder in his hand, you don't see the folder in the reflection in the window (which Cordelia uses as mirror to put on her lipstick) but you can see the cabinet. (00:00:20)
Revealing mistake: When Alonna is kidnapped, there is a vampire on the left side of the screen who is not wearing any mask over his face, though sunlight is falling on him. (00:26:00)
Revealing mistake: In "To Shanshu in LA" in season one, as Angel is pulling out of parking lot to follow the W&H Trucks, you can see his reflection in his rear view mirror (vampires have no reflections). Also odd that throughout the first season the rear view mirror is removed in some episodes. (00:31:19)
Revealing mistake: When the insect creature is crawling on the ceiling its hair doesn't falls down towards the floor, it "falls" towards the ceiling. (00:22:05)
Revealing mistake: At the vampires' nest, when Knox is talking about Gunn's team, the vampire wearing the green sweatshirt and leather vest doesn't have yellow eyes like the other vampires do. And the female vampire doesn't either later, when the two groups face off after Gunn's sister is sired. (00:22:30 - 00:35:35)
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.