It's probably the wheel balancing.

I've had the exact same problem.


It turned out that the tire dealers I used screwed up. Take your car to Mercedes and make sure you have a professional look at the wheels.

I used two different dealers before taking it to Mercedes. Both screwed up and overweighted the wheels. All this despite having a brand new tire put on the car.

Poor Wheel alignment shouldn't make your car vibrate. Just pull in one direction or cause weird tire wear.

You may also have tar or something stuck to the propellor shaft. Check this.

Keep us updated on what the problem was.

 

Update: I decided to drive my S500 until I could repeat the vibration problem on demand. This decision was to prevent me from chasing the problem by spending money inappropriately. I have now driven the car an additional 3000 miles and the problem has not resurfaced. This is very strange. I will keep all of you up to date on my continued journey.