Shudder in reverse

[dos tres]

I drove my E21 project for the first time ever today. I've spent the last 3 months getting the car road worthy. The car has new urethane subframe mounts, diff hanger mounts and trailing arm bushings. The axles were rebooted/repacked, rear bearings replaced, etc. I was expecting the car to drive like new as far as the rear end is concerned, but it has a horrible shudder when reversing. It feels like someone is taking a jackhammer to the bottom of the car, and this is reversing slowly under minimum power. I noticed a little shudder also when going forward, but I found the diff hanger bolts were loose and tightening them seemed to make it go away. Any ideas what could cause the reverse shudder? It feels like the rear subframe is hopping, but I don't see how it can with $400 worth of new urethane bushings. Could it be the center support bearing? Once in motion there is no vibration.

[BertjeConti]

Probably a propshaft linkage bearing shot

Had the same symptoms once on a volvo 164

[dos tres]

I think I fixed it. The muffler was loose, I could make it bang around just shaking it, so I tighted up the hanger. I also found that a motor mount nut was finger tight when I was replacing the 02 sensor today. It seems to be OK now. Looks like the 02 sensor cured my surging idle too.