What major problem would be associated with having no censorship of the media?
The main problem with a complete lack of censorship would have to do with issues of national security. A good example of this can be seen in the recent "Wikileaks" secrets that were published in the media. When there is no censorship, secrets that can compromise national security can be published in the media. As a hypothetical example of this, imagine what would happen if the media got a hold of our contingency plans for dealing with the fallout from an Israeli air strike on Iran. If such plans were published, the Iranians would know exactly what our plans were and could adjust in ways that would make those plans ineffective.
This does not often become an actual problem, but it is a potential problem for any society that has no censorship of the media.