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.
Heartthrob - S3-E1
Revealing mistake: When James, a vampire, chases Angel and Cordelia into the subway, James' reflection is visible in the windows of a passing train.
Heartthrob - S3-E1
Revealing mistake: In this episode both Angel's and James' reflections are visible during the fight scene inside the train.
Heartthrob - S3-E1
Character mistake: In the first flashback to Angelus and James in Marseille, Angelus briefly speaks with his modern-day American accent before reverting to his Irish accent.
Revealing mistake: Supposedly the demon Merl has no tongue, but when he is telling Angel the apology he wants, it can be seen. (00:01:00)
Carpe Noctem - S3-E4
Continuity mistake: When the gang rescues Angel and returns him to his normal form towards the end of the episode, Cordelia shocks him unconscious with a taser and he falls to the floor, lying on his front. But when Fred whacks him on the head with her baseball bat, he is suddenly lying on his back.
Revealing mistake: When Cordelia goes to see Lilah, the eyelashes of her real eye can be seen blinking Underneath her "black" eye after she sits down.
Quickening - S3-E8
Continuity mistake: Sahjhan establishes that he is incorporeal on Earth, but when he takes Holtz to meet his demon minions, he manages to knock on the door.
Continuity mistake: When Lorne covertly warns Angel that the hotel is bugged, he places a note in Angel's pocket with his hand on Angel's shoulder. When Wolfram and Hart watch the video feed later, the hand that was on Angel's shoulder is now in front of Angel's chest. (00:22:50 - 00:37:00)
Plot hole: When Angel is being pursued by the Lilliad demons, he is holding his son Connor and is talking to him in the car. Later on it is revealed that he is in fact holding a teddy bear with a bomb attached to it. If it wasn't his son, why was he talking to it? It couldn't be to fool the Lilliad demons because they wouldn't be able to hear him, as they were in separate vehicles.
Continuity mistake: When the demon Angel and Groo are chasing crashes through a wall, the resulting hole lets in enough sunlight to force Angel into the shadows. A few shots later, Wesley notices Angel standing in the entrance to the hole. Only a few moments have passed, so Angel shouldn't be able to stand where he is. (00:15:20 - 00:16:20)
Revealing mistake: When Groo rushes in to battle the tree demon, a cobweb gets stuck to the camera as it pans in.
Sleep Tight - S3-E16
Continuity mistake: Right before Holtz and his men arrive at the hotel, Angel arranges three of Connor's toys in his cot. One of them is a teddy bear which he places in the middle of the cot. But once Holtz and his men arrive, the teddy bear is suddenly at the far end of the cot resting on the pillow.
Sleep Tight - S3-E16
Revealing mistake: When Angel is seen gulping the blood from the cup (right before Lorne tells Angel that Connor needs some papa-love) you can see this is a special-effects cup (it's like one of those freezer mugs, where there's a layer of liquid on the outside). If Angel were really drinking out of the cup the way it's shown, he would have blood all over his lips and it would be running down his chin.
Sleep Tight - S3-E16
Audio problem: At the end of the episode when Holtz jumps into the dimensional rift with Connor, we hear Angel yell "no" twice. But his lips don't move on either occasion.
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.
A New World - S3-E20
Revealing mistake: The first stake that Conner fires from his stake cannon (Obviously CGI) doesn't seem to emerge properly from the barrel of the cannon, it emerges out of thin air from the side. (00:01:25)
A New World - S3-E20
Revealing mistake: The Axe that Groo throws at Conner at the start of the episode (Obviously CGI) doesn't match the movements of his hand, it leaves his hand before he actually throws it. (00:01:40)
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.