When Sidney and Tatum are talking on the porch, Sidney says, "...If I'm wrong, that means the killer may still be out there..." Tatum replies, "Don't go there, Sid. You're starting to sound like some Wes Carpenter flick." This is an inside joke about "Scream" director Wes Craven. He often jokes about how people always confuse him with "Halloween" director John Carpenter.
Casey says about the "Nightmare on Elm Street" films that "the first one was scary but the rest sucked." The first film was directed by Wes Craven, the sequels weren't. He did direct "New Nightmare", but it doesn't really count as a) it's not called "A Nightmare on Elm Street" and b) is set outside the continuity of the other films, classing them all just as films compared to the "reality" of itself. Alternatively of course she's just mistaken.
Just before the credits roll there is a brief flash of the ghost faced killer, this was a clue that there was going to be a sequel. The same thing occurs just before the credits of Scream 2 but it doesn't occur in Scream 3.
In the beginning when Casey's parents come and hear her choking on the phone, Casey's dad says "Listen, I want you to drive to the MacKenzie's house and call the police." At the end of the movie Halloween, Laurie Strode tells the two little kids she's babysitting to walk over to the MacKenzie's house to call the police.
When the principal, played by Henry Winkler aka the Fonz, is in the bathroom, he goes to comb his hair, then realizes that it's ok, just like on Happy Days.
The killer's costume in the Scream movies has come to be known as "Ghostface". When the costume's package is first shown to the Police Chief by Dewey, it is actually called "Father Death". The only time "Ghostface" is actually mentioned is by Tatum right before she dies, when she calls him "Mr. Ghostface".