Joseph Smith was human, as are all of us. You can't expect him to get it perfectly right the first time, now can you? That would be unfair, not only to him but to everyone else. So he was inspired of God, who is perfect. So what? While God is perfect, us mortals are not, a fact that was paid for in the blood of our Savior, Jesus Christ. 
 
Here's a good example. Say you're taking a test, one of those tests that they make you take both at the start and end of the school year. It'll be the exact same test both times. The first time you take it, you haven't learned everything on it. You don't understand half the questions, and you get most of them wrong. The school year passes, and you learn a lot. When the end of the year rolls around and you have to take the test again, you understand what's going on and can answer better. You would, of course, get more right on the second test, when you know what's what. 
 
So why would Joseph Smith be exempt from this? He was only a man- a prophet, yes, chosen of God, yes- but still, only a man. The first time around he did the best he could, but he did not get all of the "answers" right. As he learned more, as his friends and helpers learned more and understood the word better, he made changes to his book. Why wouldn't he? 
 
There's another point I would like to make. The Holy Bible was originally written in Hebrew (I think- it was another language, at least). So, when it was translated to Gaelic or Roman or whatever, the wording changed. Here, I'll make another example. In translating from English to Spanish, the words get a little muddied. The subject is behind the verb, or something like that. Translating it literally back into English would create what I call the "Yoda effect", with them saying something like "Powerful, he is," or whatever. So they flip-flop it to make more sense. 
 
With the Bible, when it was translated into different languages, it suffered a few mistranslations. Of course it did- we are, of course, only human. Thus, the version you are reading- whatever version that may be- is bound to have at least some mistranslations. Would you object to someone fixing those mistranslations? I should hope not. In the same way, there were most likely mistranslations in the Book of Mormon. Most of those changes are simply clarification or the like. 
 
I hope I helped. :)

I think Lisandra hit it right on the head. Through the Translation process, I don't think that anything was ever changed from what it was originally, but rather, as they found mistakes, changed it BACK to the original. Here's a little snippit on it I took from the Church's Website: 
 
Joseph Smith translated the Book of Mormon by the gift and power of God. During the process of dictating, transcribing, copying, typesetting, and printing, some human errors were made. Soon after the first printing of the Book of Mormon, in 1830, readers began finding typographical, spelling, and other mistakes. The Prophet Joseph Smith and Oliver Cowdery made over 1,000 corrections for the second edition (1837). For the third edition (1840), Joseph Smith made further corrections after careful prophetic review, comparing the original manuscript with the printed text.