Revealing mistake: In the scene where Kate finds her father dead, just after the shot of his neck wounds, she is sitting over him and you can see the father blinking a few times. (00:33:00)
Revealing mistake: When Angel stands at the cabinet with a file folder in his hand, you don't see the folder in the reflection in the window (which Cordelia uses as mirror to put on her lipstick) but you can see the cabinet. (00:00:20)
Continuity mistake: In the season one episode 'I Will Remember You' when Buffy and Angel are talking in the sewer Buffy's hair goes from being just a few strands over her shoulder to having a whole side over it, and back again. (00:11:05)
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)
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)
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: 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)
Continuity mistake: When Angel is talking to Cordelia in the garden at the very end of the episode "Supersymmetry" he has a cut on his cheek. The beginning of "Spin The Bottle" is the continuation of that scene, but Angel's face no longer has a cut.
Continuity mistake: When Gunn is talking to Wesley near the start of the episode, he mentions that he's tracked Lindsay down, and that he's been living under the name "Doyle", and holds out the lease of his apartment. There's a close-up of the lease a few seconds later, in which the name "Lindsay McDonald" can be seen.
Continuity mistake: When Angel kicks the vampire out the window, he does it with little effort and movement, but when the shot goes from outside the building, he's swinging his body like he's put more into it.
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.
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: When Cordelia is putting on lipstick she uses the windows as mirror. In the reflection we see the top drawer of the cabinet is open the whole time, but it is later opened by Angel. (00:00:10)
Heartthrob - S3-E1
Continuity mistake: In the scene where Angel has just returned and given Cordelia her necklace, watch Cordelia's hands; they keep changing position in each shot. In one shot she is trying to put the necklace on, in the next shot she appears to have given up and brings her hands down and bundles the necklace in her hand. Then when the shot changes to behind her, she is trying to fasten the necklace behind her neck again. This happens a few times during this scene.
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.
Factual error: Wesley has his throat cut, deeply enough to at least nick the artery (based on the amount of blood) and the windpipe (based on his difficulties breathing and talking later on), yet he somehow survives being left alone in the park for over 24 hours. In reality, he would have been dead long before then.
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)
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.