Hi;the short story is; Following the suggestion of several knowledgeable people, I replaced the one set of links in the rear suspension that are ' the usual suspects', and my problem, which was the rear end of the car swaying side to side, was fixed. The part numbers will be at the end of this post.
LONG VERSION: I bought a 1989 300E with 175,000miles, cheap. I suspect the car had some suspension work done in the past, because the car is reasonably tight. But, it did bounce all over the road, and was not inspiring at 70 MPH. Four new shocks worked wonders, reining in most of the motion (set of Monroes. made in Spain, $280 full set, and I am happy with them). The front end feels rock solid, and does not wander. But one problem remained. AS I came on the gas, or off the gas, the rear end would shift somehow, and cause the car to point in a different direction, requiring compensation with the steering wheel. At speed, this was unsettling. The motion was in the rear, best described as rear end sway. All of the links in the rear, and the differential mounts, and the subframe mounts looked okay. They felt okay to the limited force I could bring to bear on them. But a shop foreman, and a good parts man, both agreed that the diagonal links listed below needed replacing. After doing so, the car tracks 90% better, and tomorrow's 4 wheel alignment should help the rest.

#210 350 33 06, control arm also known as thrust arm, etc.

#210 350 45 06, Bolt kit (nesessary)

#210 352 00 43, sleeve (necessary).

The new control arm is not an exact replacement. A bushing with a smaller ID hole is used. The new arm requires a smaller bolt, with a sleeve to take up the slack where the bolt goes through the bearing carrier.
The biggest dificulty came in getting the replacement bolt to line up upon installation, since the suspension is somewhat pre-loaded. I had to use a hammer handle (correct length) as a wedge between the front of the wheel well, and the suspension, causing the suspension to move aft a half inch, which allowed the bolt to go through.

I also installed 4 new tires previous to the suspension work. I had four totally mismatched tires, but installing 4 new tires made no difference. But my new Bridgestone Potenze G009's are great in the rain.
-Paul T