I've seen estimates as high as over 5,000, describing the number of changes in the Book of Mormon from its first “inspired wording” to recent editions. But don't take my word, or anyone else's for that. Look on this site and compare multiple digital versions for yourself:

Facsimilies of Historic Book of Mormon Editions

Very interesting!

For more information, see The Mormon Mirage 3rd Edition:  A Former Member Looks at the Mormon Church Today (Zondervan, 2009). Also available as an audiobook and as an expanded-text E-book for Nook, Kindle and other reading devices.

Also available by Latayne C. Scott, Latter-day Cipher: A Novel