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: 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.
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.
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)
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.)
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.
Through The Looking Glass - S2-E21
Continuity mistake: When Angel transforms into his inner beast for the first time he is seen ripping off the right leg of an Imperial guard, but in following shot the leg is intact and it stays like that for the rest of the fight. (00:25:35)
Disharmony - S2-E17
Continuity mistake: When Harmony enters Cordelias bedroom, the strap on Corelia's shirt falls off her shoulder and then magically is back in place after the angle change. (00:13:50)
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)
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)
Disharmony - S2-E17
Other mistake: At the very end, as Angel walks out the door he reflects in the panes of glass on the door. (00:42:10)
Disharmony - S2-E17
Continuity mistake: When Cordelia and Harmony are on the couch talking and drinking, the towel on Cordelia's head goes from on her shoulder to behind in the change from wide to close up. (00:10:30)
Disharmony - S2-E17
Other mistake: When Harmony spills her pig's blood on the keyboard, the computer shorts out, and the monitor flickers off, but the mouse cursor is still visible. (00:25:35)
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)
Disharmony - S2-E17
Continuity mistake: In 'Disharmony' Willow's hair is over her eye when she says "Thanks for the affirmation", but when we see her again a second later its tucked behind her ear. The shot wasn't on Cordelia long enough for her to have tucked it back. (00:16:45)
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.