At this point, cultural institutions are aware of the power of social media. Whether it is the Library of Congress's embrace of Flickr, academic libraries use of Twitter, or museums sharing across platforms, social media is a free, easy way to share information with users and colleagues.
Google+ makes sharing even easier for libraries and museums, because it does not have the 140 character restriction of Twitter, nor the semantic baggage of Facebook. By using circles, it's easy to create groups of users and share information in a more targeted manner. Facebook does not allow lists to be created for pages. That means everything a library or museum communicates is shouted with a megaphone to everyone who has "liked" the page.
With Google+, an academic library can create various circles depending on user's interests. Is there a group of faculty interested in new acquisitions for Biology? Create a specific circle and reduce the noise of the feed. Some ways institutions have been working around this problem is to create multiple Twitter accounts or Facebook pages, as well as a plethora of blogs. It can be cumbersome and limited.
One problem with Google+ is that in order to deliver specific information to users, they need to be using Google+. Right now, it's still in the early stages; however, as users flock to the service won't they be pleasantly surprised to find your institution already has a presence?