Quick question everyone. I have a 88 volvo 244 and while I was under the car trying to replace the shifter bushings I grabbed onto the driveshaft and could turn it a pretty good ways clockwise and counterclockwise. I could turn the shaft about a quarter of a turn. While doing so, it was making some noise in the rear differential.

How concerned should I be? Is this why I hear a rather loud CLUNK from the rear end of the car as soon as I hit the gas and accelerate briskly after being totally stopped? The noise doesn't happen when I accelerate slowly.

 

It's normal to have some play in the driveshaft. What can you do about it? Well, even a newly rebuilt diff will have enough play to allow some shaft movement. Considering how plentiful used diffs are, how little load the redblock puts on them, and how long I've had really loose diffs last in cars, I'd say just ignore it.
Thumps etc on acceleration are always rear suspension bushes that are worn, dying diffs whine.