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.
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.
Cordelia: You want I should distract him? Make with the nice-nice while you slip by?
Angel: Don't be stupid. I'm that guy and the most beautiful woman I've ever seen is making eyes at me? It's either a bachelor party or a scam.
Cordelia: What did you just call me?
Angel: I'm sorry. You're not stupid.
Cordelia: No, after that.
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.