The upper control arm bushings are usually the first thing to cause the E28 shimmy. Once those are replaced, check your center link and tie rods. Autocrossing, driver schools, and even stick tires on the street can kill steering hardware in 30k miles.

Ed

My problems with the steering wheel shimmying at 48MPH was originally only under braking. So I replaced the front brake rotors with 750il units and resolved the shimmy under braking but the got it when just driving at 48mph with no braking. I had also replaced the rear stabilizer arm and inner arm due to ball joint boot dry rot...so I had 3 different garages look at the car, check alignment, balance tires, straightened 3 rims, changed from summer to winter tires, installed Dinan 750 sleeved bushings in the rear stabilizer/thrust arms, all with no difference. Then I switched back to M5 rotors and the problem is 80-90% better. But it is still there. Any ideas?