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: 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)
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.