The only notorious gotcha may be a leaky gas tank. You need to lift the tank, and inspect the weld at the rear hinge. Usually only 2000 and 2001 had that issue once in a while.
Other common faults, leaky fuel pressure regulator, and Regulator/Rectifier goes bad.
To check the fpr, just pull the small vacuum line, turn on the ignition and as the pump primes up, watch for any gas leaking from the nipple.
To test the R/R, bike not running, battery should have 13V-13.4V. With bike revved to 5000rpm and highbeam on, charging should NOT exceed 15.5V.
Those are the common things I can think of, and they are not restricted to the RC51. Other early 2000's FI Honda's suffer the same problems.
Aside from that, RC51's are damn sturdy bikes if properly maintained.