e30 Differential Replacement
I decided to replace the open 3.73 differential on my 92 325ic with a 4.10 LSD. I must say that I am really happy with the results, and would recommend the swap to anyone. The replacement is quite simple, and only took me a few hours to complete.
Before removing the existing differential, prepare the new differential for mounting in the car. If the differential is used, you might want to make sure that the rear housing mount is in good condition. If you need to replace the mount, it will need to be pressed out/in, so you should have this done before you start the swap.
I decided to put the new Z3 M coupe differential cover on:

since it includes a beefier mount and a more complex set of cooling fins. There is a comprehensive article on using the ///M coupe diff at: e30m3performance.com, including all the part numbers. If you decide to go this route, make sure you get all the necessary components, including the longer bolts, gasket, etc. The article stated that they purchased the cover from the dealer for $140. I called around to dealers in California, and the price ranged from $195 to $235. Most dealers also do not stock the part, and will need to special order it. The same goes for the bolts and the drain plugs. BMW of San Diego had the part in stock, so I purchased it from them for $195 (I was in a hurry). You can use the drain plugs from the old diff, just make sure that you get new crush washers for them. The New differential uses drain plugs that use a 14mm hex tool to remove/replace (the plugs on the stock diff are typically 10mm). I could not find a 14mm socket or wrench, so I ended up using my old ones.
I did find a company: motorsportimports.com which lists the cover for $149, so you might want to check them out. Another thing that I would recommend getting is Redline gear oil. It was recommended that I use the 75W90 oil. They also have a 75W90NS, but I was told that this might be too grippy for street use. Apparently, the only real adverse affect of the "NS" is that while backing up and turning (like pulling out of a parking spot) you may hear a "clunk-clunk-clunk..." as the plates grab and release. I decided to go with the standard oil.
Definitely make sure that you have all the parts before you begin the project, as some may be difficult or take time to get:

I put the new cover on the new diff and filled it with oil before I started removing my old one.
Jack up the rear of the car and place the car on some jack stands. I jack the car up from the bottom of the differential, but I put a flat piece of wood between the two to cushion the differential. For the time being, leave the car in gear and the parking brake on. Remove the speedometer plug:

and push the connector somewhere out of the way. If you need to remove the speedometer sensor from the housing, it is attached with 2 10mm bolts. Be careful not to damage the trigger ring inside the differential, which is what rotates through the slot in the speedo sensor.
Remove the 4 17mm nuts that connect the driveshaft to the differential:

You will need a 17mm combo wrench, as there is probably not enough room to get a socket wrench in the space. You can get to 2 or 3 of the nuts, then you will need to release the brake and put the car in neutral, so that you can turn the shaft to get to the remaining bolt(s). Apply the brake again and put the car in gear.
Next, loosen the 12 (6 on each side) bolts that hold the half-shafts to the differential:

Mine were external Torx E12, but some will have 8mm hex bolts instead. You might want to take a peek under the car before you get started, so that you can make sure that you have the right tools for the job. You can probably loosen most of them, but will then need to release the brake/put the car in neutral, and rotate the wheel, since the axle will probably be in the way of the bottom bolt. You do not need to take them all the way out, just enough that they separate from the differential.
Place a hydraulic floor jack under the differential. Remove the 19mm nut and bolt that hold the differential through the mount:

Since both sides are 19mm, you will need 2 wrenches of that size. A 1/2 drive ratchet with 19mm socket and a 19mm combo wrench works best. Completely remove the bolt from the bracket.
Next, remove the 4 19mm bolts that hold the differential in:

The bolts screw down through the bracket into the top of the differential. You can get to the lower two with either the ratchet or the combo wrench. The top two (towards the rear of the car) can only be accessed with the combo wrench, since there is not much room between the bracket and the bottom of the car. Make sure that the floor jack is positioned to hold the differential once you start to take the bolts out. Once the bolts are out, slowly let the jack down, balancing the differential with your hand. The back of the diff will need to drop down just far enough to get the mount below the mount bracket, then the diff will need to move towards the rear of the car, to separate it from the driveshaft. Once the driveshaft bolts are clear, slowly lower the differential all the way down. At this point you can pull the jack and diff out from under the car, and set the differential on the ground.
Here you can see the two differentials for comparison:

For installation, the procedure is just the reverse of removal. The only thing that is difficult, is aligning the differential up just right, so that you can get the 4 main bolts started. Once you have the differential pretty close, you can use your finger to feel through the top of the bracket, and gently move the floor jack to align the holes. Once you have the 4 bolts started but before you tighten them down completely, put in the bolt/nut for the mount. Tighten the bolts, attach the driveshaft, axle shafts and speedometer plug. I took the car out for a short test drive, then let it cool down. I put the car back up, and checked to make sure that the bolts were still tight. I also did this after 1 week, just to be sure.
Feel free to contact me if you have any questions!
Dave