Below are general notes and the coaching facts that I was unable to find, found conflicting answers or had to guess about.  The biggest problem was determining when coaches started their careers and when they retired.  If anyone has information about these I would love to hear!

All games that were vacated by the NCAA for rules violations are included in my lists because they were played and I'm nicer than the NCAA.  The "Official" record is noted in the comments.
In 1953, Kentucky was suspended by both the SEC and the NCAA.   I have treated this in the same way as NCAA vacated games and given Rupp credit for being active that year.  I don't think anyone thought Rupp was not Kentucky's coach and the Kentucky team stayed together and practiced as if it were a regular season.
In 1908, Phog Allen coached both Kansas and a college named Baker.  In 1909, he coached Kansas and a college named Haskell.  I'm not sure how he managed, but in both years, the records for each school look like he coached a full season.  Because of this, I have credited Allen with two more years (or should I say seasons) than his official record of 48 years.
the NCAA Basketball Records Books include non-Division I statistics.  I included these in the total years that coaches were active rather than trying to figure out which schools were Division I forty years ago.  Coaches whose records weren't good enough to be included in these books and were active before 1973 were found in The Modern Encyclopedia of Basketball and don't have any non-Division I years represented in my list.
Lou Rossini left NYU and ended his career at St. Francis (NY).  The Modern Encyclopedia of Basketball lists no one as NYU coach in 1972 with Rossini being the coach in 1971 so I have assumed that 1971 was his last year at NYU.  I have also assumed Rossini started at St. Francis in 1972, but have no evidence of this other than I know he coached there and the NCAA Basketball Records Book says he retired from coaching in 1979.
UPDATE 11/2002: I found a later revision (1979) of the Encyclopedia that states Rossini did not coach from 1972 to 1975, making 1976 his first year at St. Francis.
Bob Weinhauer coached Pennsylvania in the tournament in 1978, but I could find no record of when he started coaching there.  Since Pennsylvania went to the tournament in 1975 under Chuck Daly, that narrows it down to 1976, 1977, or 1978.   The NCAA Basketball Records Book lists 1977 as Daly's last coaching year (without mention of a team) making 1978 the likely first year for Weinhauer, though Daly could have coached elsewhere in 1976.  Unfortunately, The Modern Encyclopedia of Basketball only goes to 1972, so I don't know if Weinhauer coached from 1973 to 1977.
 Fortunately, a Penn alumnus emailed me that Weinhauer was Daly's assistant and took over in 1978. Similarly, 1982 was the last year I could prove that Weinhauer coached Penn, though The NCAA Final Four Records Book lists 1985 as his last active year. The Encyclopedia of the NCAA Basketball Tournament shows Penn at the tournament with a different coach in 1985 which puts Weinhauer coaching at some other school, possibly from 1983-1985. Again thanks to my friendly Penn alumnus, who suggested than Weinhauer went to one of the Arizona schools and thanks to a story about Weinhauer being fired as GM of the NBA Bucks in 1999, I was able to find out that Weinhauer coached Arizona State from 1982 to 1985.
Joe Williams was active until 1986 according to The NCAA Final Four Records Book but his last tournament appearance was with Florida State in 1980.  I couldn't find anything that said he stayed there, but I will assume so until finding out otherwise.
J. D. Barnett is credited with 20 years of coaching in The NCAA Final Four Records Book and was listed as still active in 1998, and The Sporting News BB Yearbooks lists him as active in 1999, but not in 2000, so it appears he coached 21 years. Vitale's book doesn't list him as active (in fact, makes no mention of him at all), so I presume he had some time off.  He isn't listed in the first Sporting News Yearbook (91-92) and Tubby Smith is noted in his first year as Tulsa's coach that year, Tulsa being the last school mentioned for Barnett in 1987.  Also, 1995 is listed as Barnett's first year at Northwest State.  So... I'm assuming Barnett coached Tulsa through 1991 and then didn't coach until 1995 putting his starting date with VCU (or other school) at 1976.