my completely stock 00 has a tiny amount of soot lining the tailpipe, does not leave a deposit on the concrete, I do a lot of city driving so once in awhile run it to the rev limiter, these motors need a good highway run a couple of times a month, I normally shift at low rpms in city driving. They are great city bikes but were designed for long long drives at speed
IF the only symtom is a lot of soot on start up, heavy soot deposit in tailpipe, and bad mileage AND the motor has been pushed hard/long run highway then the O2 sensor is a good prospect. If the bike always driven extremely easy it could be slightly carboned up (possible pinging) and needs a good fast highway run.
no offence meant to anyone - when I was young I used to hear mechanics talking about taking poorly running babied sports cars out for an "Italian tuneup" - run the s**t out of them - return them purring like a kitten - no parts required