Extra Continues:
To get continues, go to the game selection screen and hold L1+L2+R1+R2 and press O rapidly.

Play as Heihachi:
At the title screen, highlight start game then press and hold Left+Square+X+Start. Keep holding until game starts.

Play as Paul:
At the title screen, highlight start game then press and hold Right+Square+X+Start. Keep holding until game starts.

Black Ship:
At the title screen, highlight 'Reset' then press and hold L1+L2+R1+R2+Select. 'Game Start' should be highlighted. While still holding the buttons down, press Start until you begin the game.

Thanks to Revolution readers Pocket Man and Kauza!