Some quick suggestions off the top of my head:
Giant Flywheel. For resistance to bumps and bruises, spin up a giant flywheel to help you conserve momentum.
Traction Control. This was mentioned before, but I'll summarize the idea of a traction control system. In a car, you compare the speed of the powered wheels to the unpowered wheels. If there is a difference, that means one set is slipping while the other isn't. The computer cuts a bit of power to the driven wheels until both spin at the same rate. For a 4-wheel vehicle, you can use an accelerometer to get the differential measurement.
Mariocart for Driver Training. Mariocart
invented drifting. Blue sparks may be a safety hazard, though.
Pneumatics as Thrusters. Satellites use gas thrusters to control direction. If the surface is low enough friction, this could act as a nice stability augmentation.
Antilock Brakes. Antilock brakes don't necessary cut down on braking distance, but rather they give you control WHILE braking. If you slam on a car that doesn't have antilock brakes and you lock the wheels, the car basically keeps moving in the direction of its momentum vector, regardless of which direction the steering wheel is pointing (conservation of momentum). With antilock brakes, you're switching between static friction and dynamic friction, and in a nut shell, this gives you some control (ie allows you to swerve around the object you're braking for).
Physics 101. Actually, Physics 8.01. For the truly adventurous, check out Walter Lewin's physics videos on MIT's OCW, specifically the lecture dealing with friction.
http://ocw.mit.edu/OcwWeb/Physics/8-...il/embed08.htm. This is roughly equivalent to an AP Physics class.