In 1979, Paul Gebhard and Alan Johnson of the Kinsey Institute at Indiana University spent years "cleaning" the data of suspected contaminants (some of which are mentioned in dan04's answer). Their results were published in The Kinsey Data: Marginal Tabulations of the 1938-1963 Interviews Conducted by the Institute for Sex Research (1979), portions of which are available online via Google Books.
This excerpt lists some of the individuals excluded from the re-evaluation of Kinsey's data (the groups mentioned are the sample divided by college education and race):
All of these groups were cleaned in the sense of removing individuals who had derived from sources with known sexual bias. By known sexual bias we mean a group which we know to be substantially biased in some sexual way before we began interviewing its members. Examples include the Mattachine Society (a homosexual orginization), the occupants of homes for unwed mothers, prostitutes employed by a famous madam, personal friends of individuals known to be sexually deviant, and patients in mental hospitals. Also, all individuals who had been convicted of any offense other than a traffic violation were excluded since we now know that such individuals (as a group) differ in terms of sexual attitides and behavior from persons who have never been convicted.
However, the changes only led to a handful of differences. The authors attributed many to the improved statistical methods they were able to employ in the reevaluation, but some to the "cleaning" of Kinsey's data:
In another example, the effects of the cleaning of the sample were evident. The incidence figures of homosexual activity for single and married college-educated males, Table 90 in the Male volume, are quite similar to those of this volume, but our current noncollege sample has much lower incidences than Kinsey's grade-school and high-school-educated samples. A major cause of this discrepancy is clear; Kinsey's noncollege samples included persons who had been incarcerated in jails and prisons (where homosexual activity is relatively common) whereas our present sample excluded them.
Despite these differences, the authors maintained that no significant conclusions produced by the earlier Kinsey studies were debunked:
Despite the flaws of our earlier pioneering publications and the difficulties of comparing them with this volume, it is clear that the major findings of the earlier works regarding age, gender, marital status, and socioeconomic class remain intact. Adding to and cleaning our samples has markedly increased their value, but has not as yet caused us to recant any important assertion. In using our new Ns in analyses, we anticipate we will discover relationships previously unknown to us and we will undoubtedly have to modify some prior statements, but we feel the important contributions of Dr. Kinsey will stand.
As an example, the original Kinsey study indicated that 37% of males has had at least one homosexual experience to orgasm. The re-evaluation placed that figure at that 36.4%. The original study only found that 4% of the white male population to be completely homosexual (a 5 or 6 on the infamous Kinsey scale), while the re-evaluation placed that figure at 9.9% for the college-educated group and 12.7% for those with lesser education, astounding considering opponents expected that latter figure to be much smaller after omitting convicts.
Most resources criticizing Kinsey's work fail to take this re-evaluation into account at all, so it's hard to ascertain whether they missed anything or not. All of the flaws in Kinsey's original work seem to be accounted for. Furthermore, no study of this magnitude has been conducted since. Kinsey's study is by no means perfect, but neither has it been conclusively debunked.