Level Select:
When you see the words "Press Start" at the Title screen, press C-UP seven times.

Alien Disruptor :
Beat level 7 on Expert difficulty.

View Chopper :
At the Chopper Select screen, highlight (don't select) a chopper and then press L. This will take you to a screen showing the chopper rotating. You can control the chopper's rotation using the control stick.

View the President :
During a game, press Z, C-UP, and C-DOWN at the same time and the launch a homing cluster. The President will jump out if it hits.