Continue:
Hold I + II and press Run at the "Game Over" screen.

Extra lives:
Stand at least five block lengths away from a lamp post, then jump while kicking to hit the post perfectly.

Hidden level warps:
Locate the brick bridge on level 1-4B. Kick the right corner of the bridge and underneath. This will allow game play to continue in fields 2, 3, or 4.

Locate the area halfway through level 3-3B where two rats begin to follow your character. Jump on top of them to reach the two bricks, then jump up. Game play will resume at 6-4.