The facsimiles of the 1840 and 1842 are both available on this website. There are other editions of the Book of Mormon printed during the life of Joseph Smith, but to the best of our knowledge, these are the last editions printed before Joseph died.
The 1840 Book of Mormon was carefully revised by the translator, Joseph Smith Jr. The 1842 edition of the Book of Mormon was printed using stereotyped plates created from the typeset of the movable type of the 1840 Book of Mormon. All printing and spelling errors are the same in both editions. There are two differences on the title page: the date was changed from 1840 to 1842, and the Jr. from Joseph Smith’s name was dropped in the 1842 edition because Joseph Smith Sr. had died in September of 1840.