Visible crew/equipment: When Angel is fighting the demon, you can see an obvious camera and two hands in the bottom right corner. (00:27:10)
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.
Trivia: In the opening credits there is a shot of a girl standing alone on the corner of a street. This was taken from the Buffy episode "Anne", when Buffy was staying in Los Angeles.
More trivia for Angel
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.
In The Dark - S1-E3
[Watching from on top of a building as Angel talks to a woman he just saved, Spike guesses what is being said.]
Spike: [as Rachel.] How can I thank you, you mysterious black-clad hunk of a night thing?
[as Angel.] No need, little lady, your tears of gratitude are enough for me. You see, I was once a badass vampire, but love and a pesky curse defanged me. Now I'm just a big, fluffy puppy with bad teeth. [Rachel reaches for Angel's head.] No, not the hair. Never the hair.
[as Rachel.] But there must be some way I can show my appreciation?
[as Angel.] No, helping those in need's my job, and working up a load of sexual tension and prancing away like a magnificent poof is truly thanks enough.
[as Rachel.] I understand. I have a nephew who is gay, so...
[as Angel.] Say no more. Evil's still afoot. And I'm almost out of that nancy-boy hair-gel I like so much. Quickly, to the Angel-mobile, away.
More quotes from Angel
Question: If Angel didn't experience a "Moment of Perfect Happiness" from his night with Darla, why does he go through the same motions he went through from losing his soul before?
Answer: Due to his epiphany, Angel basically had the 'true darkness' he worked so hard to reattain ripped away from him, like his soul was after sleeping with Buffy.
Question: In the opening credits, just before the shot of Phantom Dennis, is the shot of the girl crying Darla? What episode is that from?
Answer: Nope, it's not Darla - that's Rachel from the episode "In The Dark", the third episode of the show (the one with Spike's magnificent opening monologue).
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.