Walkabout makes many good points and outlines things to be aware of when buying a used bike ... any used bike. Sometimes we must just go on faith.
Sure, there are so called "anti- BMW" folks around but I see more Crack Smokin' BMW Zealots than anti's.
The F, G and X series singles have been popular bikes, been around decades, many have done RTW or ridden them to high kms. Are there issues?
Yep ... and going onto the forums and READING is probably the very best way to really learn the bike and all it's history and possible issues. Like most bikes, do the maintenance and problems tend to disappear or are reduced.
One addition to Walkabout's comment on the forks: It wasn't just early F series that broke forks off ... the documented occurrences show forks snapping off from early F series Funduros up to current G model bikes. They all (apparently) use a similar Showa fork ... that fork (to my eye) looks under sized for a near 500 lb. single. How could BMW not address this issue and switch to a bigger, stronger fork?
One German guy sued BMW and won a settlement. There was also a class action suit in Europe, don't know the out come. Suffice to say, the documentation on the snapping off forks is there by actual owners. So it's not some urban myth.
Would I worry? NO! It's still a rare occurrence.
We had 3 different F series test bikes at the magazine when I was there. I only rode one of them. Later rode with buddies riding F650GS's, Dakar et al.
No 1st hand experience with current G650's.
Other prominent issues are over-charging from faulty Regulator/Rectifiers that would cook the non sealed cheap battery BMW insisted on using long after every Japanese OEM switched to sealed MF (maintenance free) batteries.
Check your stator output ... if it's over 14V, look into it ...
Wire harnesses can also BURN UP due to this and other electrical faults. A low battery will also affect instruments, ABS and will trigger F.I. fault codes. So a strong, fresh battery is a must.
The basic Rotax design motor is basically good save the water pump issues. Always carry a spare on board. Some F.I. issues. If the Water pump goes out you can easily blow a head gasket ... and you could lose the whole motor if you don't catch this early.
Many freaked out when BMW switched production of the F650 motor from Berlin to Loncin in China, where they've been made for over a decade and continue production there today. Very good motors in general.
Other major complaints in the F650's and Dakars are wheel bearings. Many reports of failed bearings. I've no idea why. Once again, to get all this and much more, get onto the forums the spend a week catching up on 20 year production history.