About 7 seconds into the opening theme you see the face of a young man looking up (Just before you see Angel with the sword) That young man is Phantom Dennis. He is only seen once in episode 5 of the 1st season- Room with an Vu. After that he's an unseen "character" until season 4.
In the episode "Underneath", Illyria is talking about different dimensions she has visited and she says "And one world with nothing but shrimp...I tired of that one quickly." This is a reference to Buffy episode "Superstar": when Anya is explaining that there are many types of alternate realities, she says, "And there could even be a world with nothing but shrimp."
Angel leaves the Reaper locked in a metal cage as the camera pans slowly back so we can only see his eyes - almost exactly the same shot as when Connor left Angel trapped in the metal coffin at the end of "Tomorrow". They even say the same thing - "You get to live. Forever". Like father, like son.
In the episode 'Untouched' Angel asks Cordelia 'Do you have any idea how hard it is to think when you've got a rebar through you?', her reply of 'Actually, I do. Benefits of a Sunnydale education' is a reference to the BTVS episode 'Lover's Walk', in which Cordy falls through a staircase and is impaled on a rebar.
Angel's headquarters in season 2-4 was in the Hyperion Hotel. Hyperion is another name of Helios (the god of Sun in Greek mythology), and means "the one who goes above".
To illustrate where her speech is placed on the itinerary, Fred compares it to a baseball player batting between Nomar Garciappara and Sammy Sosa, who both played with the Chicago Cubs. While Garciappara wouldn't join that team until well after the episode aired, and nobody could have known what would happen two years in the future, it's not a mistake; but as a Cubs fan, I find it an interesting choice of comparison.
When Angelus taunts Connor about trying to kill him and then sleeping with Cordelia, he comments, "Screwing your mom and trying to kill your dad? There should be a play." This refers to the Greek tragedy "Oedipus," in which the eponymous character unwittingly marries his mother after killing his father.