I use Redline synthetic 75W90 gear lube
Redline is recommended for either regular or limited slip diffs. My E320 is a regular diff but I have traction control, which uses the ABS system to prevent excess wheel spin. Currently I'm trying to remove the drain and fill plugs. They appear well-corroded into place. I found a useful thread in the archives with lots of good tips. (Such as remove the fill plug first) I couldn't locate a 14mm allen wrench locally, so I'm trying to jury rig one by having a friend weld together a 9/16-inch (wrench size) number 8 hardness bolt and nut. The hardware store bolt we first tried was like taffy. Next step is to call the Snap-on man for a socket wrench version.
94 E320 Wagon, 170k, totalled in 2006
2002 BMW 525i Wagon, 75k
1991 BMW 318is (two of 'em)