One of the more noteworthy provisions of the proposed legislation is that it calls for blocking entire sites to deal with infringing content. This is unfortunate in terms of collateral damage: A site like LiveJournal could be blocked over content that I (as a user) have no control over, as a consequence of going after "bad guys". (A similar mechanic is active in the recent takedown of Megaupload. I'm sure there was infringing content, but there's a lot of inconvenienced non-infringing users as well.) Sites with a lot of user-generated content would be in trouble, especially if it's uneconomic to have a site administrator police everything. Wikipedia would essentially have to shut down, as a most visible example of the problem.
From a economic viewpoint, though, this is a pretty good example of the tragedy of the anti-commons. Unlike the similarly-named case with no property rights, a case of overlapping property rights can lead to under-use of a resource. SOPA would extend the property rights of intellectual-property holders to include the privilege of blocking content that is merely co-located with infinging content. Given the number of potential rightsholders to negotiate with, this blocks off a lot of useful activity. It also does so at a less-direct level: Where is the line drawn between infringing and non-infringing content? With lots of people to potentially offend, a lot of now-legal parody and commentary becomes legally risky. Yes, it's legal, but you have to argue that after they shut down your site ... so why bother in the first place? (This chilling effect is probably a significant motive behind the legislation in the first place.)
As a side issue, adding new legal processes (paths outside the judiciary, DNS blocking requirements for ISPs, etc.) deserves careful scrutiny: It is claiming, more or less, "Due process is too much work." On the contrary, due process is vitally important.
All of this is orthogonal to the question of exactly how much protection intellectual property should have; Even if it needs still more protection (I don't think it does), the proposed mechanisms are a poor way to accomplish that.