At the Mode Selection screen, press L, Z, R, C-Up, C-Down, C-Left, C-Right, Start. You'll hear a chime if it was done correctly. Now you'll have all the cups available (including the Hidden X-Cup and Joker), all 30 cars, and the difficulty level, Master.
At the car selection screen, press and hold L, R, and all four C buttons. You will see the car shrink, and now you can play with smaller cars.