Revealing mistake: During the whole slow motion fighting scene in the bar the punches clearly miss their targets.
The Cautionary Tale Of Numero Cinco - S5-E6
Revealing mistake: When Angel says to Wesley that "Fred has got something," and then walks out of the room, Angel's reflection is visible in a window pane in front of him. It's very brief, but it's there. (00:31:05)
Continuity mistake: After Wesley, Cordelia and Gunn sing "We Are The Champions" and Cordelia mentions tequila being evil, we see Wesley put aside some shot glasses. These glasses change position three times throughout the rest of the scene without anybody touching them.
In The Dark - S1-E3
[Watching from on top of a building as Angel talks to a woman he just saved, Spike guesses what is being said.]
Spike: [as Rachel.] How can I thank you, you mysterious black-clad hunk of a night thing?
[as Angel.] No need, little lady, your tears of gratitude are enough for me. You see, I was once a badass vampire, but love and a pesky curse defanged me. Now I'm just a big, fluffy puppy with bad teeth. [Rachel reaches for Angel's head.] No, not the hair. Never the hair.
[as Rachel.] But there must be some way I can show my appreciation?
[as Angel.] No, helping those in need's my job, and working up a load of sexual tension and prancing away like a magnificent poof is truly thanks enough.
[as Rachel.] I understand. I have a nephew who is gay, so...
[as Angel.] Say no more. Evil's still afoot. And I'm almost out of that nancy-boy hair-gel I like so much. Quickly, to the Angel-mobile, away.
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.