Prophets are not infallible. Some thoughts: 
 
- A prophet himself is not infallible. He is human. He has opinions and thoughts that are not always right. But when he speaks as a prophet - then we can know that what he says is true. The important distinction is to know when he is speaking as a prophet and when speaking as himself. 
- Many of the comments that some people say are reversals are really the result of mis-quotes, things taken out of context, etc. 
- Here is a great article talking about what is doctrine:  
Mormon Doctrine 
 
So the question is when is the Prophet Speaking as the Lord? Here is a quote from one of our scriptures. It is in Doctrine and Covenants Section 68:  
3 And this is the ensample unto them, that they shall speak as they are moved upon by the Holy Ghost.  
4 And whatsoever they shall speak when moved upon by the Holy Ghost shall be scripture, shall be the will of the Lord, shall be the mind of the Lord, shall be the word of the Lord, shall be the voice of the Lord, and the bpower of God unto salvation.  
 
God definitely is infallible. We His children - even including His prophets - are not infallible. That is one of the reasons we are here on earth is to learn and experience life and try to become more like God and to slowly and steadily become better and better. 
 
Lastly let me also say that the Prophets and Apostles (esp.those in our modern day) are some of the best and most righteous men who have ever lived on the earth.