This one was fun and productive. My rear differential was leaking at the base of the cover, and rather than simply topping the diff off with fresh fluid, I wanted to change the seal and get rid of most of the junk gear oil in there. I pulled the cover off the rear differential. Leaving the top two bolts in, I popped the cover and drained the old, nasty fluid out. 
It smelled rather burned/carbonized, but the ring gear wasn't chewed up and there were essentially no shavings in the drained fluid.I then cleaned out the gears with some shop towels, wiping out as much of the old gear oil as I could. I think, overall, it went well. As part of this process, I also cleaned the flanged on the differential
housing with a 1" chisel (gently, as not to gouge the housing in any way). It had a thin, crusty layer of RTV on it, as well as an old gasket saturated in certain spots where it was leaking (near the bottom). My primary concern was to get a good, smooth flange. I was considering using some sandpaper but thought better of it. In hindsight, I should have used a small level to check how true the differential housing was.
Afterwards, I turned my attention to the cover, which needed to be wiped clean of the old fluid and bits of RTV and gasket. I scraped its flange smooth, using WD40 in small doses to loosen the built up RTV. I also used a file to remove small nicks in the leading/outer edge of the flange on the cover. I assumed some were there from the previous owner
hitting the occasional object while four-wheeling. All in all, it took about fifteen minutes. I just sat on my driveway, scraping and filing away. I then put on some new RTV sealant, followed by the new gasket. Once I was finished with this, it was put back on the Jeep and filled with Lucas Oil's gear oil for limited slip differentials (which apparently is different than regular gear oil).________________________________________________
I then had to turn my attention to the pinion seal where the pinion comes out of the differential to meet up with the yoke where the rear drive shaft attaches. As you can see in the pic at left, oil and grime cover the bottom half of the differential but there's almost none on the drive shaft itself. This a typical sign of a bad pinion seal. 
The oil leaks out here and thenis blown back onto the differential housing by the wind flowing underneath the Jeep. At first I was worried that there was too much slop or play in the pinion shaft, which would beat up the pinion seal and lead to a leak, even if I put in a new seal. Luckily, that was not the case. First, I had to remove the drive shaft from the yoke, for obvious reasons. This was easy. I want to lube up the U-joint anyway, so popping off the drive shaft gave me the opportunity to clean up that joint area a bit.
The only real pain in this process was removing the U-joint from the pinion shaft. There's a large nut down the center of the joint which holds it onto the pinion shaft (you can see the hint of a nut in the above pic and the threads in the pic at left). It is a compression fit (the shaft gets wider as it moves down into the differential), so as the nut is tightened (to 200 ft-lbs.), the U-joint is pressed down onto the shaft. Even after the nut was removed, it was as if I hadn't taken it off yet. I used AutoZone's tool loan program to get a five-ton puller. Eventually, it popped off, but not until I'd put a great deal of strain on it. I was afraid the thing would blow up in my face as the pitman-arm puller did early in my Jeep work. It didn't.
Now I got to pull the old seal, which was a mess (see right), and then put in the new one. Putting everything back together was fairly easy. The only issue, if you can call it one, was
getting that nut tightened back to 200 ft-lbs. I have a very good torque wrench that goes up to 250 ft-lbs., but I couldn't get the dang thing to "click" at 200. I read on IFSJA.org that 200 ft-lbs. really means "as tight as humanely possible." Lying under the Jeep, both hands on the torque wrench above me, slightly above horizontal, I was lifting my large frame off the ground, pulling with all that I had in me at this point. I'd put thread locking fluid on it, so I'm quite confident it won't back out on me. It hasn't yet. In the end, the seal remains clean to this day, and I'm happy with what I got done.