Level select
Press Up(3), Down(3), Up, Down(3), L1, R1 at the title screen.

Big head mode
Press Up(3), Down(3), Left, Right(3), L1, R1 at the title screen. Alternately, Get 30 licenses in arcade mode with any character, then press Square + X at the character selection screen.

Another arcade mode
Get all 36 licenses in arcade mode, then press Circle at the stage selection screen.

Additional characters
Hold R1, R2, L1, or L2 at the character selection screen.