When adjusting your character's stats, pay special attention to cornering; slaloming is the easiest way to lose a good lead.
Game music
Play track two and higher of the game disc in an audio CD player to hear music from the game.
Hard Turns
Use hard turns sparingly (L1 and R1); although they are necessary in spots, too many can blow your course time in the space of a few seconds.
Play as Mr. Chicken
Successfully complete all ten courses on any stage with all five standard characters using the same saved game file to unlock Mr. Chicken as a playable character.
POV
While it's easy to skip past them, replays can offer invaluable info about the courses that you won't see from your third-person POV.