We have a 2012 F650GS, owned since new.
It's a fantastic street bike, but as an Adventure bike, it's capabilities are on par with a V-Strom - power about the same as well. Will handle light gravel roads fine, but the only thing that's favourable for taking it on gnarly tracks is the upright seating position. The real Adventure model in the line-up is the F800GS and the suspension is the biggest difference between the two bikes, with the F8 getting longer suspension travel, higher clearance and a 21" front wheel.
We've taken the F650GS over some tough terrain and the suspension lets the bike down, the tires spending more time in the air than on the trail. In Mexico, the speed bumps (topes) are excessively tall, and the low-clearance 650 was continually scraping the bash plate - on the street!
Cast wheels are prone to denting and cannot be repaired like the 800s spoked wheels. We dented one (again on a pothole in the street) and had to get the wheel replaced.
Known issue for that vintage is the stator overheating and failing, which also happened to us on the road. There's a re-designed flywheel which ventilates a lot better. Check with the owner if the original has been replaced with the new design, if it hasn't, it's a very expensive fix (~ $1500 parts+labour).
If you are going to take the bike into the dealership for service, be aware that the F650GS is one of the more expensive BMW bikes to service in terms of labour. There are lots of plastic and fiddly bits to remove to get to the engine and it's not as straightforward as the boxer engines with its exposed cylinder heads. They'll charge you about an hour's worth of shop time extra for the same maintenance interval service. My R1200GS was consistently ~$100-$200 cheaper than the F650GS at the dealership.
Not applicable if you're doing the work yourself. Parts are parts, not any more cheaper or expensive than any other BMW parts.
Bottom line, it's a very good bike. I wouldn't hesitate to buy one as a street bike if one came up for sale for a good price.