Likely cause: Drive shaft center support bearing is loose or broken.
How to check: Put the car in the air and remove the heat shield near the center of the car. If you don't see any nuts holding the center support bearing to the car, that's most likely your problem. If you can't see where those nuts should go, grab the driveshaft and shake. If it moves, your bearing is either disconnected from the car (you need to find those nuts) or it is damaged.
Repair: If you're lucky, the nuts are gone and you can replace them (don't forget the loctite). If you're unlucky, your center support bearing is shot, you'll need a new one.
More center support bearing guidance from C R Kreiger:
Greg, I think you ought to edit/expand on this one to include more symptoms (a banshee-like shrieking noise under your shift lever) and the guibo vibration (on manual gearboxes only) as well. Most of the center bearings I've seen were firmly bolted in place - but the bearing failed (thus the noise) and/or the rubber support tore out, allowing it to bounce around down there. As well, the guibo is right there, always has to come out to change the bearing, and is cheap, too.
In addition, the M30 has that big harmonic balancer that can come apart and produce absolutely horrifying noises as it whacks the shift linkage, driveshaft, and the tunnel. If you don't already know, the easy solution is to take it out and throw it away for three reasons:
1) You have to buy a new one,
2) It's a PITA to reinstall and
3) The car doesn't really need it.
--
C.R. Krieger
'88 535is
'Da Red Dog'