Level Select:
During gameplay press Z,R,L,and A simultaneously to skip to the next stage.

Hidden Character Select:
At puzzle mode select screen press Left,Left,Up,Down,L,R,L,R,L+R.This will bring up a Character select screen where you can choose between the two dino's as well as some bosses

Another Puzzle World
At the Main Menu press L,Up,R,Down.When done correctly a tiny character will appear in the lower right corner.

Select Start Game now and when you select Puzzle Mode it will say Another World.