Are there no problems in other countries? In Germany the politics and media are trying to make MMA look brutal and inhuman. They even wanted to forbid the UFC in Cologne this year.
Even after the Cologne show there were still mostly bad articles, e.g. insisting that MMA isn't a sport, that there are basically no rules ("everything is allowed"), that most of the spectators are skinheads and have tattoos etc, which is a ridiculous.
I'm sure there are problems. There are many misconceptions about the sport of MMA. Both logically and statistically, it is safer than boxing. There are many different ways to win an MMA match. The goal in boxing, however, is to pound your opponent to the head and body with 16 ounce gloves, which actually cause a fighter to take more sustained damage.
I think there are a few reasons for the misconceptions. Firstly, UFC bouts take place in a cage. Without having seen an MMA fight, that sounds brutal to the uninitiated. In reality, it's no more brutal than a fight taking place in a boxing ring. Secondly, there's still a stigma attached as a result of the early, no-holds-barred days of the UFC. Now, that was vicious. The sport is nothing like it was then.