From the post announcing it, ArtShare on Facebook!:
What can you do with ArtShare? Well, you can select works from the Brooklyn Museum collection to display on your profile. But then, because social networking is about connecting and seeing what others contribute to the social fabric, anyone can also use ArtShare to upload their own work and share it with others. You can use ArtShare to select a wide variety of work, then each time your profile is loaded a different work will be displayed at random from your selections.
They contacted contemporary artists who still held copyright over their works and asked if they would give their permission for this use. They've even offered their application functionality to other museums:
If you work at another institution and want to share your museum’s collection this way, we can set you up with your own tab in ArtShare. When we set this up for you, your institution’s logo will be displayed alongside the works that you upload, so they are easily identifiable as being a part of your collection.
So congratulations to Mike Dillon and Shelley Bernstein at the Brooklyn Museum, and thank you for letting us know so that we all get to learn from your experience.
(Actually I've just noticed one problem - given the recent fuss about Facebook, advertising, applications and privacy, I wanted to read the application Terms of Service, but you have to add the application to read them, so you have to agree to them before you've read them. It's not a criticism of their application as I'm sure this isn't specific to ArtShare but I guess it does show that concerns over Facebook's privacy model are going to affect how cultural institutions engage with it.)