Is it a carb? If I recall, '01 fuel injected bikes had the MM fuel injection (no Delphi yet) and some folks don't like that. I have no experience with it though.
Check to see if the dealer sold and serviced the bike. If so, check the service records. Also, get the name & # of the former owner & contact him. Most dealers will be happy to provide you with the info.
I have a 2001 Ultra and it has served me well. If you don't plan to do a major engine build up, the Magnetti-Marelli fuel injection will work fine. It can have a few quirks but for the most part, they are easy to fix. I am replacing the tensioners on mine right now. The bike has about 20k miles on it and I could have easily gotten another 10k to 15k miles. Since I had it open to check them, I am going ahead and replacing them as well as putting in a SE 204 cam. Good luck.