Free Play mode:
Beat the game to unlock Free Play mode, which allows you to play any level without losing data.
Secret Kyoto Stage:
In the last stage (Karamusa Keep), knock the Odama through the gates of the keep to be transported to a secret level resembling modern-day Kyoto, complete with Nintendo HQ. You can use the Odama to get Nintendo workers for use in the final battle. To get back to the last stage and resume where you left off, let the Odama roll into the gutter.
Thanks to Revolution Readers Mustached and Bobby!