At the title screen, press R2, R2, R2, L1, Triangle, L2, L2, L2, R1, Square.
Face off Mode:
Beat championship mode once to open "Face Off" mode against the Roadster.
Beat the Roadster in Faceoff mode to unlock it.
Get Tow Truck:
Beat the Tow Truck in Faceoff #2 to unlock it.
Beat the Saloon GT in Faceoff #3 to unlock it.
Beat the bus in Faceoff #4 to unlock it.
Thanks to Revolution reader Bill, Fastguy, Raj Raion, Eric & Ted!