You should be able to determine the wear on the gears by the oil that comes out. There should be some (and I mean very little) metallic flake in the oil. This is a normal characteristic of the differential after say 100,000 miles. The flake should be "sugar fine" in size.
If the flake is large "snowflake" size (about 1.5 mm or greater in size), then the unit has been run very heavy and/or low on lubricant. If this is the case, I would recommend opening the unit and having a professional evaluate the gear condition for rebuild or replacement.
I would not open the rear cover (commonly called a "hogs head" cover) unless I suspected a problem. Normally, the only maintenance is the seal replacement on the input and output shafting, which is not to difficult.
Be sure to check the bushings on the moustache bar while you have the differential down. They wear and cause significant vibration which usually gets blamed on the rear end.
Have fun.