The simple fact is, they should know what content they have licenses for, and what content they don't. Maintaining a list of the top 1,000,000 bands in the world and not letting anybody upload tracks with metadata that included those bands and song names in it would not be that difficult. The data is there, because otherwise users could not search for those band names and find what they're looking for.
Simply put, if Grooveshark did everything they could to fight copyrighted material being added to their site, they wouldn't have a business. Maybe now that they have some licenses and an audience they could survive, but they would have never gotten to where they were without significant illegal content being uploaded and accessed by their users.
I addressed this in my other comment, but as it turns out, this aspect of the problem is incredibly difficult. Metadata can be wrong and we can't always depend on it. So we use waveform analysis. But thats difficult too due to the indexing and storage requirements and the accuracy of the algorithm performing the search. Also this list is not finite. It changes constantly and parties are always bickering over rights to content and that takes time to sort out. We actually have a team of people who handle takedown requests, and we have another team of people who put in the necessary restrictions to keep content from getting played or uploaded.
Also, what's waveform analysis?
Within 5 minutes I can go find music on Grooveshark that is there illegally. It ought to be pretty easy for you to do the same queries and prevent that from happening. Would you prevent legal music? Yes. What is more important - that some cover band be allowed to post their music, or that Primus be allowed to retain their rights? Particularly when you consider that nobody is coming to Grooveshark to hear covers of Primus.
I'm not saying that operating legally in the music industry is easy - far from it. But on the spectrum of trying to, unprofitable Pandora is on one side, and Grooveshark is waving hello in the far distance.
I remember Napster attempting to create a system to block subsequent "sharing" of known copyrighted works.