One gotcha about checking for play in the balljoints is that the weight of the car must be on the control arm when you do the check. Otherwise, the upward force of the spring will eliminate any play. This is different from the typical MacPherson strut setup.
If your car tends to get very unstable at speed, particulary on a rutted highway, your balljoints are the primary suspect. Groaning noises during low-speed turns, or going over low-speed bumps are another clue.
When I got my state inspection recently, they checked for play the typical way. My balljoints are pretty new anyways, but I didn't say anything...
While you have just one wheel in the air, check for play in the steering linkage (grasp wheel at 3 and 6 o'clock, and see what gives).
The idler arm bushings (on the right side) tend to be problematic.
After that, there are so many balljoints in this steering linkage that can fail... I have observed that the outer tie-rod joints seem to fail first.
Best of luck.
1986 300E 5-Speed 240k mi.