Nicolas Cage actually taunted the rest of the cast of "Fast Times" by bragging about his Uncle Francis Ford Coppola- he told all the other young actors that he would be famous faster than any of them, because he had the connections. After a few weeks of this, the cast started to strike back at Nicolas by doing imitations of Robert DuVall in Apocalypse Now, which finally got Cage to stop bragging about his famous family. My brother was an extra in all the high school scenes, and saw this happen. He also said that Sean Penn was dating Pamela Springsteen and Eric Stolz was dating Jennifer Jason Leigh, and Phoebe Cates was dating Timothy Hutton who was always hanging around.
The cast of the film said Nicolas Cage (Nicholas Coppola at the time) was in the film because of his uncle & some of the actors would stand outside his trailer & recite a version of Robert Duvall's famous line from Apocalypse Now "I love napalm in the morning," altering it to "I love the smell of Nicolas in the morning."
Spicolli's dream sequence was actually written and filmed after the film was wrapped. After beginning the editing process, Amy, Art and Azimoff realized how great Spicoli had been acted by Penn, and that they needed to beef up Penn's role in the film.
Penn had to fly back to LA, in between another job in Chicago. Because Cameron wrote the lines the day of the shoot, they used cue cards offscreen to help Penn. The cue cards of the infamous lines 'Those guys are fags!' hang to this day on the walls of Cameron's home.
Two versions of the pool scene were filmed: the one shown in the theaters where Phoebe Cates undoes her top as soon as she exits the pool, and a milder version where she doesn't undo it until she's embracing Judge Reinhold, so her breasts aren't visible.
I saw the second version on TV and can't help but wonder if it was purposely filmed for future TV showings.