It is well built and basically safe, but there are plenty of winding sections and some quite abrupt changes in elevation. You may find yourself going slower to enjoy the scenery. That's fine, but don't let cars stack up behind you. Stop off at one of the frequent overlooks for a few minutes. You'll clear up the jam and have a chance to enjoy the view, wildflowers, a trail, or an interpretive display.
Weather changes rapidly in the mountains.
Summer thunderstorms can be extremely powerful and come on very suddenly. It's best to find a safe spot and park until the storm passes. Fog is another, and very dangerous problem. First off, you will rarely see real fog. What happens is clouds get low enough that they cover the mountains.