Continuity mistake: In the final fight, Angel gets stabbed on his right side. In the slow-motion bit before his opponent chooses not to fight any more, the wound switches to his left for one shot. (00:36:40)
Factual error: According to the show, Angel learned quite a few languages when he was evil. However, when he tries to start a conversation with a red-faced demon, he makes terrible mistakes. He said "Hablo Espanol?" which literally means "Do I speak Spanish?" and he said something like "Are you from Byelorussia?" in a tongue that hardly resembled Russian, although according to the captions, it was said in Russian.
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)
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.
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)
Continuity mistake: In the rooftop scene, Buffy's hair is partly tied back and slightly curly but by the time she reaches the Police station it is completely loose and much curlier.
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)
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)
Blind Date - S1-E21
Character mistake: Angel comments that Vanessa was acquitted because of a hung jury. A hung jury means the jury couldn't come to a unanimous decision; the case would require a new trial, while an acquittal means the jury found her not guilty, and she couldn't be tried again for the crime.
Continuity mistake: When Wesley is explaining that Angel feels like he doesn't belong in the world, the amount of donut he's holding changes. (00:13:30)
Continuity mistake: In Season One Finale, "To Shanshu In LA" when Wes is lecturing Cordy on wants and desires, the number of bites taken from the doughnut changes, in one instance it breaks in half, most visibly when Wes takes a bite from Cordy's doughnut on the angle change. (00:13:31)
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)
Continuity mistake: In the season one finale "To Shanshu in LA," near the end Angel is fighting Vocah in the mausoleum and Angel rips off Vocah's mask, revealing the maggoty face Underneath. In subsequent shots of Angel from behind Vocah, you can still see the edges of the mask on his face. (00:34:30)
Visible crew/equipment: At the end of the episode where Wesley is studying the Shanshu scroll in Cordillia's apartment, the boom mike appears at the top of the frame TWICE.
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.