I'm just starting out with working on my '89 244, so I will do my best to describe what's happening...

On starting the engine (after it's been off for a while), I get a weird, loud grinding vibration from the rear of the car. This starts when I'm in park (not touching the brakes), and continues (with a little variation) when I put my foot on the brake, shift into reverse, and back up - but then it almost immediately disappears when I put it in drive and take off. It's pretty loud, and I can't really tell if it's coming from left, right, or center.

Looking under the car, I couldn't see anyplace where the exhaust is making contact with the body, or anything else obvious. I did notice that the differential (at least, that's what I think it is, dead center on the rear axle) seemed wet - not actively dripping, but slick to the touch all over. Could this be related to the noise? I'll check the diff. oil level this weekend.