Yes, they made the episode in Norway. They probably borrowed the MP5 from the police. Private ownership of full auto guns is rare. Not absolutely impossible, but rare. More common in Finland I think, which is probably what Cosmo is referring to.
HerrWolfe, Scandinavian gun laws have nothing to do with wartime occupation. It's about shooting culture, which we have more of than perhaps anyone else.
Anyway, about the TV show. I saw it yesterday. That "other guy", James I think, actually looked like he knew how to handle a rifle. Especially if he actually hit that many targets without "help" from the producer. And Clarkson was probably following orders and shooting into the snow. The targets are designed for .22 and fine tuned for international competition, spraying them with 9mm would have messed up things. I'd say the owners of the stadiums were very cooperative as it was...
By the way, the motorized full auto biathlon was not a new idea. Some years ago (possibly during the 1994 Olympics at Lillehammer), a pair of Norwegian media personalities pulled a stunt involving a snowmobile and a 50 round belt through an MG3, although they didn't do it at the actual biathlon stadium.