Right now, under the DMCA, a copyright holder can request a website remove material he or she owns. If the website refuses, the matter can go to court.
SOPA gets around this by allowing the third party to go directly to advertisers, credit card companies, and ISPs to effectively shut down a website’s lifeline when it’s suspected of posting copyrighted material. There’s no need to go to court either.For example, under SOPA, a copyright holder can go directly to Google and ask them to block all Google ads from a website that is suspected of carrying copyrighted works. If it’s a commercial site, credit card companies and services like PayPal have the right to block all payments.

It’s a classic “shoot first, ask questions later” move, and has the potential to be harmful to sites and services such as Dropbox that depend on user uploaded content.

Some other alarming bullet points from SOPA:

• Search engines can be required to block accused websites from results.

• Internet service providers can be required to block accused websites from their customers.

• Payment companies don’t need a request from a copyright holder to block a website. Instead, they can do so on their own if the suspect a website may be posting copyrighted work without permission.

You can read the full bill here for more detail.