Some pre-2004 R1150RTs had surging problems, as one of the posters above noted. I have owned R1100RTs, R1150RTs, and R1200RTs -- none of them surged at all, though perhaps I was lucky. I have never experienced surging personally.
In 2004, BMW went to the two-spark engine in the R1150RT, although a very few late 2003s had it as well. You can tell by the design of the valve cover. You can see the differences here: http://bmwmotorcycle.home.att.net/1150.htm
So ... ride the bike a variety of speeds and see if you detect surging in the engine. Most likely, you will not -- but you might. If you do, pass it by.
Other than that, just check the normal things you would on a used motorcycle. The 77K miles is not scary, if it was well maintained. Check the maintenance records on the bike -- who maintained it and how often? Did a dealer to it every 6K miles?
All this nonsense about the LT vs. the RT is just that -- nonsense. I have owned two LTs, and they were great bikes. I ride RTs now primarily because the weight of the LT was a little intimidating and because I have been a boxer nut (not numb) since 1967. By now, the boxer engine just feels normal to me, and has for decades, and I like the feel of one. A four-cylinder engine seems weird. But that's just me.
Tucson, Arizona, & Madison, Wisconsin
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Founder, Madison (Wisconsin) BMW Club, #1 (1968)
Co-founder, BMW Motorcycle Owners of America, #115 (1972)
Co-founder, Vintage BMW Motorcycle Owners, #2 (1972)
Co-founder, Wooden Canoe Heritage Association, #1 (1979)
Motorcycle Safety Foundation, Chief Instructor (1994)
Friend of the Marque, BMW Clubs International Council (1999)
Prof. Gerhard Knöchlein BMW Classic Award (2013)
R1200RT • R1250RT • 1967 R60/2