Does anyone else have what I can only characterize as a lot of "slop" when they put their 300SD in "Park"?

For example, when I come to stop, then place it in park, the car will slide forward, or backward, depending on the slope, maybe 6 or 8 inches. Of course, the tires aren't moving, it's in the tranny somewhere. It's unnerving, and it locks up my ignition key sometimes.

Is that the flex disk going bad, or the tranny, or both, or is it somewhat normal?

83 300SD 174K