Successfully finishing all ten of the missions in mission mode will unlock the Homer Car. The car is available in any mode when you select Homer's picture in car select.
Hidden New Year's Character
This cheat is simple. Set the system date on your Playstation 2 to January 1st, and the New Year's Krusty will be unlocked under the "?" at the character select screen.
Hidden Halloween Character
Change the system date to October 31st to unlock Halloween Bart in the character selection screen under the "?".
Hidden Thanksgiving character
Setting the system date to November 22nd will unlock the Thanksgiving Marge under "?" in the character selection screen.
Hidden Christmas character
Setting the system date to December 25th will unlock Christmas Apu under "?" at the Character selection screen.