The biggest risk at the beginning is privacy. You now have none. The US government will have the right to acquire information on any individual that it decides may be some type of cyber terror threat without any form of judicial process between it wanting the information, and receiving it. The fact that most of the world use US based/owned systems, like Facebook, this means that the US government has access to this information.
Down the track, it's easy to see how say a movie company trying to prosecute can argue that the government has access to information they need as part of their case, so nothing stops their courts from requiring their government to provide information that previously may not have been available.
Complicate it further and say perhaps they decide that one of us is a cyber threat because we disagree with their government, and perhaps because we have above average computing skills - we live in a country that has extradition treaties with them, so they can request us to be extradited on the basis of flimsy evidence that they have no context of. All this without a judicial process in place that might have stopped it from happening in the first place. Just a secretive government organisation that has powers to hold us without charge for long periods of time while it uses its new powers to relieve us of our privacy and twist and turn details of our lives to suit their own charge against us.
What it looks like on the face of it is nothing compared to what this can become. They have a fairly loose definition of what is a cyber threat. Anonymous have been labelled as cyber terrorists, despite the fact that a large proportion of Anonymous couldn't hack themselves out of a paperbag with a machete. A large chunk of that group won't have even tried. It wasn't that long ago that Anonymous were more notorious for protesting out the front of the Church of Scientology buildings, and for taking them on.
Most of them aren't cyber terrorists - they're just individuals who want to make the world right, to fix the wrongs, and know that strength comes in numbers.