Night Racing:
Hold L1 + L2 + R1 + R2 while selecting a track. You should see headlights appear in front of the car. A new symbol will appear to confirm.

Track Select:
Pause the game and enter the "Sound" option. Highlight "FX Volume" and press L1 + L2.

Upside down tracks:
At the track selection screen, press L1 + R1 + X + Down. A new symbol will appear to confirm.

Faster cars:
At the track selection screen for a two-player battle, press X + Square + Triangle + Circle. A new symbol will appear to confirm.

Jumping cars:
At the start of a multi-player race (during the countdown), press Circle + Left.