Only idea I have is to take the cover off and inspect the gears and look for broken pieces at the bottom of the housing, have you checked the brakes back there?
What year is the mustang?
Or....the control arm bushings are shot but...until you give us some more information its hard to help. When does it do it? Taking off, around a corner, when you brake, randomly, or any combination? What year car? Has any work been done to the rear end that you know of or is it completely stock? See where I am going with this?
It's a 2000. I checked the gears and that is the problem also the pin that goes in the differential was bent it has 2.73 I bought 3.73 but the new pin is a bit bigger what do I need to do?