I'm assuming that since this is a 07 mustang that it has a factory posi and not a spool.
Ford posi's units need that really stinky friction modifer junk put in there, if you just filled it up with regular lube then this may very well be you problem.
If you dont have it in the rearend it will make all kinds of funny noises popping, chattering and whining.
The stuff you need is at the dealership don't use the friction modifer stuff at autozone, it will not work.
Also the factory recommends a snythetic lube, I believe its a 75w-140 and its not cheap either @ around $15 quart.
NOTE: I always use more than what the factory recommends - usually 12 to 16 onces of the stinky stuff will do the trick.
Goodluck, Charles