Servo assisted brakes (whizzy brakes as they are known) can be a PITA. IIRC, they were mostly '04-07. There is a guy that rebuilds the ABS control module for a few hundred dollars. FYI - if the whizzy brake ABS module goes out, it still brakes just fine, just without ABS.
I have a couple BMW motorcycles, '86 K75C and a '09 R1200GS Adventure. Really like 'em. Do all my own work and don't find the parts to be any more expensive than other bikes - unless you have to get into special items like control modules and drive shafts. BMWMOA (Motorcycle Owner Assoc.) has a very good website with an excellent knowledge base.
Rear drive issues were generally taken care of in '09 when BMW reapplied a vent in the pumpkin. The original specs called for too much lubricant and it would take out the main bearing. They can be repaired and/or rebuilt but it is costly. Not as common as the internet would lead you to believe.
Keep in mind, most of my experience is from the Iron Butt crowd which puts on LOTS of miles.
Stock seats - awful - just like most bikes (including the Venture). Sargent makes a good seat for them if you want to do normal mileage. If you are interested in doing Iron Butt miles, Russell Day-Long is the best choice. Laam Saddles also makes a good custom seat for a bit less money than the RSL.
The K engines are really solid and perform well. As mentioned before, check for service records. Things I would be concerned with is drive shaft spline lube and brake fluid flushes. Check the bottom of the engine/transmission for signs of leakage. The transmission is a cassette style with the dry clutch sandwiched between the engine and transmission. If any of the seals at the back of the engine or front of the transmission are leaking, it is possible the clutch got wet - replacement time. Not hard to do, just very time consuming.
I will be doing the transmission seals on my '86 K bike this winter. Overall, these bike are fairly easy to work on.
The K1200LT is a real mile muncher. Nice bike with good ergonomics for taller folks (I'm 6'3" and 260-ish lbs).
RR