Checking the rear wheel i find that i have some sideways movement. Has anybody pulled final drive apart and replaced the bearings and shims. Or should i get it done by a bmw mechanic.
Firstly are you sure that the slop is in the final drive? if the wheel is sloppy then i'd be suspecting the wheel bearings, not the final drive.
Final drive bearings do not go quietly, they run in an oil bath and have a long service life - when they do pack it in (usually because water got in) they tend to howl, groan and rumble to let you know that they are buggered.
Not a difficult job to replace, easier on the pre-1980 than later, but you will need a selection of shims and I'd buy several gaskets as you will be pulling that puppy apart a few times to get it right.
But please check your wheel bearings before dismembering the final drive.