Infinite Ammo
Pause the game and enter R1, L1, R2, R2, L2, R1, L1, R2, and L2. Repeat to turn it off.
Invincibility
Pause the game and enter L1, L1, L1, R2, L1, R1, R1, L1, and R2. Your car will be invincible. Repeat, and your car will be damageable again.
Unlock All Missions and Weapons
To unlock all missions/weapons, go to the Front End main menu page and enter the following controller sequence: L1, R2, L2, R1, R1, L2, R2, L1.