There are a lot of gears back there, all with a bit of back lash. Consider, ring and pinion gears, two side gears, two spider gears. Total of 5 mesh points. Not to mention the possibility of slight play in the axle splines.

How many miles on the car? Assuming they never get run dry, these rear ends are usually good for a half million miles or more.

And no, there is no simple adjustment.

To add to that, limited slip does away with the spider and side gears, so you'd have less play. Further leading to the slim chance that you have that...

And don't listen to me.. follow what others say about determining if you have limited slip :)
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-Matt I ♥ my ♂