Jim,
Welcome to our world. The old "Airhead" bikes are pretty solid but have a couple of weak spots and a few things that require periodic maintenance to keep running smoothly.
Weak Spots:
Transmissions - Seems like the average life expectancy is between 50k and 75k miles. Some folks have run well over 100k with no problems and others much less. Drain the gear oil from the tranny and inspect the magnetic drain plug. A ball of very fine fuzz is OK if you can't feel any particles. If you feel grit, or see shiny specks it's probably time to find your wallet.
Valves - Before about 1985 BMW had not quite figured out how to make exhaust valve/valve seats play nicely with unleaded. Inspect the edges of the exhaust valves and if it looks like you could shave with them it's probably valve job time. If they look to have meat then adjust, and check after 1000 miles, if the exhaust clearances have gotten smaller then it is likely the valve seat receding. Once this gets to the point where you have to readjust after less than 1k miles it;s probably time for a valve job. R65 engines have some history pertaining to exhaust valve head seperation, that would be a bad thing.
Maintenance:
Brake System - Needs to be flushed once every one or two years. If not then you will likely wind up with a mess.
Transmission input splines - Need to be greased every few years, depending on your climate, or they will wear out.
Normal fluid/lube changes - You now have a driveshaft carrier tube and final drive to remember to service.
Rear wheel splines - Every year or two (normally with a tire change unless that only happens every 5 years!) clean and regrease the splines that mate the rear wheel with the final drive.
Swingarm bearings- Grease the swingarm bearings at least yearly. They are tapered roller bearings and can notch into their races.
Steering head - This needs to be greased periodically - again depemnds on your climate, how it's stored, etc. It's not uncommon (it's usual, really) for an older bike to need this even if low miles. The grease will harden and the steering will feel notchy and it won't handle well. Get fresh grease in there or risk wearing out the bearing races. These are also tapered roller bearings.
Other maintenance items will be related to their jap cousins - oil changes, tire balance, etc.
Have fun!