Each one is a learn as you go, something humans excel at even if it's a 16 year old kid who just got their license. This is the Achilles heel of automated driving and we're quite a number of years away from sorting it all out.
You could reasonably address this to some degree by marking the temporary lanes with colored paints. Presumably, these problems will mostly be solved by automatic routing. Your car will just go around, whenever possible. It will know there will be a delay there. Obviously, sometimes that's not possible, which is why the human is going to have to intervene in some situations for quite a long while. Since most of those situations are going to be at quite low speeds, though, the driving controls can recede in importance. Perhaps a force-feedback joystick really will become a viable car controller, at least for vehicles which are expected to drive themselves almost all of the time.
In theory, the orange cones could have RFID or some other technology added that can be polled indicating that it's in a construction zone. Much like the invisible fence for the iRobot vacuum cleaners.
As for routing around, this works fine for passenger vehicles but no so well for trucks. There are routes that trucks are prohibited from taking due to bridge height, weight restrictions, etc.
I still think that the biggest challenge is weather. A system that works well in clear dry weather quickly falls apart in a heavy downpour, fog, and during the winter with snow and ice obscuring lines, signs, signals, etc. In fact, winter also presents the additional challenge of obscuring camera lenses and getting salty water on external sensors, etc. Obviously, Nevada was picked because it presents the fewest weather challenges.