Four continues:
Quickly press C, R, Right, Down on the start/options screen.

Zone select:
Press Z, Down, L, Up on the start/options screen.

Auto-fire:
Press B, Up, L, Right on the start/options screen.

Hidden difficulty levels:
Press L, Right, Down, Left on the start/options screen. The "Abnormal" and "Very Easy" difficulty levels are now unlocked at the options menu.