Are movies released in the cinema polished or edited coming to dvd?

I went to see the Hobbit last week and loved it. However there were a couple of small mistakes, such as a couple of CGI swords clipping through robes. Although these things are small, and do not matter that much I was wandering. Will these things be fixed or edited out before coming to DVD or is the movie we see in the cinemas the same thing that will be on the DVD?

Thanks. ;)