Chris,
In my opinion, there are definitely safety issues with Spyders, much more so that Speedsters. Because of the low ride height and curvature of the body panels, they are very difficult for oncoming drivers to see, particularly in traffic. Add a silver, silver/blue, or gray color and the problem is exacerbated significantly, particularly early or late in the day.
The same factor also serves to make it difficult for drivers turning across your path or entering your lane from a side street to judge you closing speed. That being said, you should not only be wary of people cutting your off, you should drive as if you EXPECT it to happen.
Additionally, the height of the body (28-30 inches at the top of the door) makes it extremely difficult for people in larger passenger cars, pick-ups and SUVs to see you in their mirrors, and increases the likelihood of being cut off in traffic or run over in parking lots. Just the other day, I watched in horror from inside a store as a woman in an Expedition came within inches of backing all over my Spyder...She never even saw it becasue the top of the car was below the range of any mirror on her vehicle.
Finally, just know that any crash with a speed in excess of 20-25 MPH will likely result in severe injury, if not death. No consideration is given to crash worthiness when these cars are constructed. If you find yourself paying attention to those who say that this or that brand is safer because of the way it is constructed, just get in the "safe" car and pull up to any full sized car or pick-up so that it is positioned as in a 90 degree side impact and see where the other vehicle's bumper is. That will tell you how safe you are in a collision.
Yes, I have one of these cars and it is great fun, but it is about as safe as a motorcycle in a crash, and people can probably see cycles better. You just have to be very, very careful.
Again, just my opinion.
TMc