The Driveline
The BMW transmissions
Manual transmissions are reasonably tough, as well as the clutch. The only usual problems are bad second gear synchros and possible a loose output flange or bearing noise. The last two are rather serious problems, the first a common problem that most people just live with. The loose output flange problem affects all pre-'76 cars, before BMW improved the design of the output shaft and flange. By now, most cars have had their transmissions rebuilt, with the new style shaft and flange. A little bearing noise is acceptable, but excessive noise is usually a sign of impending failure, usually of the rear layshaft bearing. New bearings are now roller bearings, instead of ball bearings, which can withstand greater loads.
The BMW differentials
Differentials are usually reliable. Problems here are seal leakage, whining, and broken spider gears. Seal leakage problems are almost universally common, and should be left alone. Minor whining is also common, and should be left alone. Broken spider gears are not all that common, but do happen. The result is that the differential becomes locked, and no longer allows a speed difference between the two wheels. Installing a used differential is the simplest remedy for this problem.