According to Pat Beall via the Cox News Service, a website called Wii Have a Problem has started to share stories of people who don't know how to use a Wii controller without flinging it across the room and breaking something. The article is more serious in tone than the website, going so far as to quote a Wall Street Journal article which cited people "complaining of sore elbows and wrists after especially vigorous gaming sessions."
Not everyone is a flailing loon, however. KB employee Alex Parus explained that he "put the wrist strap on and then I threw my arm as hard as I could," wherein nothing happened. No wii-motes flying into television screens or soft baby skulls. "Unless people are damaging it somehow, I don't see how [the wrist strap] could break," he said.
The lesson from all of this is to temper your enthusiasm for the Wii before you or something else gets damaged. If you're about to dislocate your shoulder, you are not playing correctly.