We now fully use and accept the "Inspired Version" (often called the JST or "Joseph Smith Translation").
Originally, the manuscript of the Inspired Version was in the hands of the Reorganized Church of Jesus Christ of Latter-day Saints (RLDS) and thus we could not be sure that their documentation was accurate. Recently, however, they have given us access to the original manuscripts and we could verify the veracity of their information.
We will probably continue to use the KJV primarily, however, for two reasons:
1) It helps us communicate better with the rest of the world
2) The KJV is in remarkably good condition considering how many translations, etc. it went though to get to us.
So, what we have done is provide the JST in the footnotes of our KJV. For example, look at Matthew 4:19.
Here is a link to the verse in the digital edition of the LDS scriptures: http://lds.org/scriptures/nt/matt/4.19?lang=eng#18
You'll note that there is a footnote ("a") in front of the word "Follow." If we look at that footnote, we see the following:
"JST Matt. 4:18 ...I am he of whom it is written by the prophets; follow me..."
Thus, Joseph Smith "repaired" the verse that reads
"And he saith unto them, Follow me, and I will make you fishers of men."
in the KJV to read
"And he saith unto them, I am he of whom it is written by the prophets; follow me, and I will make you fishers of men."
in the JST.
There are two primary reasons the Spirit seemed to direct Joseph to change a verse:
1) The verse in the KJV is corrupted either through mistranslation or deceit.
2) The Lord wanted to clarify the meaning of the verse.
The change in Matthew 4 above is likely of the first kind. It seems, for whatever reason, part of this verse was left out at some point in the many translation processes.
I added all of that above to show that we have used the JST for quite some time. A pictorial example of the above may be found here:
http://seminary.lds.org/manuals/old-testament-seminary-student-study-guide/ot-ssg-2-iv.asp
Many who read this may also be interested in this video:
http://lds.org/ldsorg/v/index.jsp?autoplay=true&index=2&locale=0&sourceId=1a98747631f92210VgnVCM100000176f620a____&vgnextoid=bd163ca6e9aa3210VgnVCM1000003a94610aRCRD
We do not "seldom speak about what got changed in this bible version." In fact, I've had several lessons on it in the church. It is most often used as a study tool. The change is generally done to teach us something. In this vein, you may want to read this account of how the Lord showed Joseph to change a verse in the Book of John:
http://lds.org/scriptures/dc-testament/dc/76?lang=eng
(particularly note verses 11-12 and 15-19)
After the change in the verse was given, it caused Joseph to marvel and he began to ponder on what had been given. Upon doing this, the Spirit gave him further revelation and we have the rest of the verses after 19. This is generally the same reason we have the JST - to provide us something to examine, ponder, pray about, and to seek knowledge and revelation about.
I hope that helps! Please feel free to e-mail me! You may also be interested in the following:
http://lds.org/scriptures/gs/joseph-smith-translation-jst?lang=eng
http://lds.org/ensign/1997/08/the-joseph-smith-translation-plain-and-precious-things-restored?lang=eng
http://lds.org/liahona/1980/09/the-bible-and-its-role-in-the-restoration?lang=eng
http://lds.org/ensign/1981/10/the-church-publishes-a-new-triple-combination?lang=eng (scroll down to the section on "footnotes.")