Taliban and American aid. After the September 11 attacks, it was necessary for conservatives to somehow explain away the fact that the US government gave 245 million dollars to the new evildoers du jour. Never mind the fact that authors such as Robert Scheer warned of aiding the Taliban as early as in May 2001. Never mind that they did so not out of some humanitarian motivation, but because of the Taliban's violent enforcement of the ban on opium poppies. Never mind that in a regime that is controlled by warlords, it does not matter who is authorized to distribute the aid -- the ruling regional warlords will seize control of it and use it to their own advantage. Never mind that this very argument has been used by hawks in opposition to sending humanitarian aid to Iraq's Saddam Hussein. Never mind that the Taliban continued selling opium in spite of the deal. Never mind that this is all documented on Michael Moore's website about the film. Gun homicides. Statistics are Moore's weakest point, and it is surprising that his critics don't dwell on them longer. That's because they know all too well that Moore is correct: The United States have a far greater homicide rate (both gun- and non-gun) than most other first world countries. His main mistake is that he does not use population corrected data, his second mistake is that he does not cite his sources (and, as you correctly point out, he probably uses different reporting methods for the different countries). A good comparison of international homicide rates can be found on the relatively neutral guncite.com website. 
For what topic does Michael Moore fail to cite his sources?
The United States Homicide Rate (Both Gun and Non-Gun)