Revealing mistake: You see Cordelia and Wesley walking without Angel through the gym in the mirror (because vampires have no reflection). In the Widescreen Edition you can see Angel waiting at the right side of the screen to join in a "normal" shot. (00:02:45)
Revealing mistake: Just after Angel kills the quan-eyed demon, he exits the room behind the smashed mirror. On the widescreen DVD you see Angel's reflection in the mirror to the right of the smashed mirror (even though vampires don't have a reflection). (00:03:40)
Continuity mistake: Right after Cordelia has her vision, Wesley goes to the whiteboard. In the "Case" column he writes "N.D.U.O." Underneath what looks like "CARYNSS" crossed out. But once they find out that it is a Prio Motu demon and Angel writes it on the whiteboard, "N.D.U.O." disappears even though Angel did not rub it off.
Continuity mistake: When Angel writes "Prio Motu" on the whiteboard and says that they need to find it and narrow it down to somewhere, Wesley says "I may be able to help us with that." In the immediate closeup of Angel, his stance has suddenly changed. In the previous shot he was standing with his arms straight down and his hands close together, but in the closeup they appear to be as though he has his hands on his hips.
Visible crew/equipment: When Angel is fighting the demon who protects the pregnant woman, at one point a crew member (in ordinary street clothes) shows behind them for a few frames.
Visible crew/equipment: When Angel gets on the horse to joust, you can see a part of a camera at the right side of the screen. (Widescreen Edition)
Are You Now Or Have You Ever Been - S2-E2
Continuity mistake: When Angel hides the bag of money up on the shelf in the basement, he is not wearing glasses. However, in the close up shot of his arms and the bag though, he is.
Character mistake: In this episode, Gunn wonders how he could have lived in Los Angeles all his life without knowing about all the "weird ass stuff" going on. But flashbacks in "Double Or Nothing" show that he knows demons exist there.
Other mistake: In the episode "The Shroud Of Rahmon," when Angel changes into his vampire face, his teeth don't change into fangs. (00:33:55)
Revealing mistake: In the scene where Angel fights the demon for the first of his trials, upon cutting the demon in half for the second time he chains the two halves to the walls. When he drags the upper half of the demon to the wall, the green legs of the actor are momentarily visible, when they should have been removed by CGI. (00:29:00)
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.
Blood Money - S2-E12
Continuity mistake: In season three episode "Anne" of BTVS, The character "Anne" who later comes to season two of Angel running a youth shelter had a rather large red tattoo of half a heart on her arm. However, no trace of it is to be found when she is on Angel. Tattoo removal is a rather pricey procedure, and she seems to be tight on cash until she gets the two million. Even if W&H would have paid for the procedure, there would be some scarring or residual pigments for such a large tattoo. (It's definitely the same character - Anne says that she used to think vampires were cool, until she met one. That's a reference to her first appearance (as "Chanterelle"), in which she belonged to a vampire-loving cult.)
Blood Money - S2-E12
Continuity mistake: During the charity event when it shows the birth year and death year of Holland Manners, it suggests he was 49 years old when he died. But in an earlier episode, he attempted to sacrifice his daughter for his 50th birthday.
Revealing mistake: When Wesley accidentally turns off the power, the room briefly goes dark, then lights up with moonlight/streetlight from outside. In the real world, that light would have been visible the whole time in the background. (00:01:45)
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.