I'm with Renegade. They've only solved the (relatively) easy part of the problem so far.
Their tests so far were just on dry pavement, as far as I can tell. But I would expect that given proper data (accelerometers for detecting unanticipated yaw and impending hydroplaning, input from wheel speed sensors to detect slippage, visual input to detect e.g. approaching ice) that the problems of inclement weather could be handled. In the long run, I bet the computer can do it better than a person thanks to its fast reaction time and immunity to panic. In principle, the computer could also have discrete brake inputs for each wheel (or at least each of two brake lines), allowing for finer control than is possible with just one brake pedal.
I think the biggest challenge is noticing and interpreting the "body language" of other drivers, in order to anticipate problems and thus avoid them before they become critical. Frequently a human can tell that someone is about to change lanes, just by observing the way that other driver behaves. The same is true for other behaviors.