When Brandon and Brenda get ready to go to the club they tell their parents they are going out but are intentionally vague about their destination. But later when Brandon is telling his parents about the mishap with his car, Cindy says "I thought you were going to the movies."
Brandon: That's what my life is about, working my butt off to pay for the damage I inflict on my car.
Steve: I'd like to exchange this egg.
Worker: What's wrong with it?
Come Inside by The Thompson Twins
Dominion by The Sisters Of Mercy
The Beginning by Seal
Go! by Tones On Tail
Brandon: (talking to Brenda and Dylan who are leaving the underground club) Hey, hey, hey, come on, guys! Don't go away mad!
Emily: Just go away.
The dialogue alludes to a Mötley Crüe song "Don't Go Away Mad (Just Go Away)". It was released on the album Dr. Feelgood in September, 1989. Interestingly, the song itself contains a reference to an earlier song by the band, "Too Young to Fall in Love."