Nick Carter auditioned for a spot in the same lineup as Britney Spears, Christina Aguilera, Justin Timberlake and Ryan Gosling. He was offered the part but turned it down because he'd been invited to help form a vocal group which eventually became the Backstreet Boys. MMC was canceled a year later.
The only cast member who didn't return for the final season was Keri Russell. She left the series to film Daddy's Girls (1994), a show that didn't make it through its first season.
Jessica Simpson and Matt Damon tried out for, and came very close to getting, spots on the show. They were beaten out by Britney Spears and Christina Aguilera.
Kirsten Dunst, Ben Affleck, Ryan Phillippe, Brittany Murphy, Joey Fatone (Justin Timberlake and JC Chasez's future *NSYNC bandmate), Donald Faison, Sara Bareilles and Countess Vaughn all tryout to join the series but were rejected from Disney.