The type of oil used is not a factor in the leaking.
3 possible sources:
1) 'Residual' dripping from messy job (mechanic did not cleanup oil spilled on outside of diff).
2) Leak around fill or drain plug (not installed tight enough).
3) Leak around cover gasket (mechanic may have removed this to inspect gears)
Clean the diff with spray brake cleaner, then let it sit a while.
You should then be able to determine where the leak originates.
1986 300E 5-Speed 240k mi.