Make your racer small:
When your on the character select screen, go to whatever character you want to race as,
 then hold Y and press A. Your character will shrink down. Now when you race you'll be small.
And if someone runs over you. . .your still small! A fun little trick.

Continue Driving in Battle Mode after your defeated!:
This is a cool little trick me and my brother found out years ago.
Sometimes when your hit with a shell for the last time, to lose your last balloon, if you keep holding gas, and don't let go, you'll continue to drive around. Your screen will dim and everything, but you'll keep driving.

Change Camera in Replay:
Play a Time Trial Race, then select a replay, click L or R to change the Camera Angle.