This is really neither here nor there, but I wonder if the original owners didn't follow proper break in procedure for the differential. 2500 burbs are almost always bought for the purpose of towing heavy. They could have hooked up to a heavy trailer and headed down the road with 50 miles on the clock.
The electrical problem would concern me much more than the rear differential, as you will never know when you will be stranded, and you will not know if it's fixed unless you find the "smoking gun" which is not easy on these newer vehicles.