The most dangerous thing around this area are drunk drivers. The roads are small, perpetually wet, winding, and not banked, so driving too fast can be incredibly dangerous.
The wildlife can also be somewhat hazardous, although with a bit of common sense, most danger can be avoided. This is bear country, so make noise if you are travelling in an area with limited visibility most of this area has very poor visibility, due to the extreme amounts of vegetation. Also, cougars do live in Olympic National park, and are much more aggressive and dangerous than bears. That being said, the number of incidents involving mountain lions is very small, so there isn't too much to worry about. Another animal that needs to be watched out for are the elk. Although elk are herd animals, and not aggressive like their moose cousins, they can be extremely dangerous if they feel threatened. Only an idiot would threaten a herd of 50 elk though, so if you are not an idiot, you will be safe from these animals. And if you are an idiot, then you get to take part in one of the most ancient aspects of nature - natural selection. Most people do not see bears or cougars, but you need to be prepared.
On the coast you need to be in good shape, in many places the coast is extremely rugged and you need to have good reflexes as you go across the headlands for when you slip. You will need to pack everything with you when you go in, and pack almost everything as you go out. Basic backpacking rules must be followed by the park's rules.
