Quick outline of some problems:
- SOPA will give copyright holders power over foreign companies. If there's an organization based in a foreign country that's engaging in illegal online trafficking with citizens in the U.S., the government gets authority to barge in and try to shut it down. That's like China walking in and arresting the CEO of Apple for threatening its electronics industry.
- Third-party hosting sites are going to be absolutely screwed over. Sites like YouTube, Vimeo, and Mediafire become liable for what their users uploads, so if someone uploads a copyrighted video, guess what? They get sued. Their userbase is large enough that there's no possible way they can control everything that's posted.
- SOPA will actually hurt a great majority of businesses more than it will help. Companies will have to invest in a bigger legal department to handle lawsuits, taking away from their capacity for other ventures.