86 R65 w/70k miles. After approx. 10 miles the rear of the bike (driveshaft/u-joint?) begins to ride 'rough' that is, feels like it is shuttering (my best feeble description). Could the u-joint be going bad? Ideas?
Could be a number of things - all bad sadly.
Firstly you need to eyeball the whole thing, I think that your 86 is a monoshock, I've not ever pulled one of these rear apart (but expect I will do so in the future as I now harbour an oilhead) but I am aware that the mono rear end is somewhat more prone to bearing failure than the dual shock iteration. Fortunately replacing the bearings in a final drive is well within the capability of a determined home mechanic (there is a video on youtube of someone successfully re-habbing their final drive in decidedly 3rd world circumstances.
If it is the shaft a number of people offer exchange services on refurbished shafts, if you can find an Emerald Isle reseller they will have a new replacement part at a fraction of the price of the BMW part and which has a good name for reliability.
If I am wrong and you have a twin-shock, the bearings are less likely to have failed, but you still need to eyeball your final drive - disassembly is covered by Snowbum and is also on youtube. A twin-shock shaft is a throw away and replace according to BMW, but who listens to them. The major problem is sourcing the universal joint which is extraordinarily difficult to find (but can be if you are persistent and tenacious) the sort of good news is that the universal joints used in a number of Honda "quad bikes" is near identical, unfortunately they do come at a honda spare part price.
As BMW did not expect the universal joint to be replaced they simply staked it in place instead of using circlips to retain it - this means that whoever works on your shaft must carefully machine off the staking so that the old joint can be removed in the usual way, they must then fit the new joint and carefully and accurately center the joint and then figure a way to retain it - the usual way is to spot weld some suitably sized washers to retain the joint.
Alternatively of course you can simply buy a 2nd hand shaft, given a clean environment the joint does tend to last a very long time.