To avoid taking damage from a high fall, perform a hip-drop (L button) before landing.

Sliding (B button) on a wet surface is the fastest way to travel without a special nozzle. Have Mario spray the ground in front of him, then press B to dive into the wetness. Keep holding forward on the Control Stick, and Mario will continue to slide as long as the ground is relatively flat.

After beating the game, talk to the Piantas who are so eager to give you a pair of sunglasses. Along with the shades, they'll give you a special shirt with a now-familiar design...