I have been playing with Facebook Graph Search for a few days now. It certainly isn't the Google killer that a lot of sites have played it up to be, not yet at least. My overall first impression: A nice improvement to the user interface, but lacks meat on the bones yet.
From a design and user experience perspective, I love it. It integrates into the original, familiar blue bar seamlessly. They removed the search box and left only a place to type. If anything, this will make Facebook easier to navigate to things I do not have shortcuts to already. +1. The default search options are all pretty useful. They give you, with no typing required: My Friends, Photos of my friends, Restaurants nearby, Games my friends play, Music my friends like, Photos I have liked. All of the options seem pretty optimal for content discovery.
The Graph Search is most useful for finding people interested in the things that you are interested in. My first test search was for "people who like air hockey."
The results are quick, but it is not a one step search. If you are not searching the standard categories like "restaurants," the engine doesn't recognize the context very well. You are presented with options to clarify what you mean. Were you looking for air hockey the interest? The game? A person? A group? Google has an enormous head start on recognizing intent of queries and has spoiled us in finding what we were looking for before we really even knew ourselves.
Once refined, it is simple to discover someone who shares an interest. You can exclude your friends from a search and find people who you don't know and enjoy the same things.
My second intuition was to find some pictures related to my interests. I looked up both "air hockey pictures" and "disc golf pictures" but was unable to find any usable results. You can look up pictures of your friends, pictures you have previously liked and even pictures near you, but I never found any interesting disc golf pictures.
Next, I wanted to see how it did with some local search queries. With very general categories, it did just fine. I was able to look up local plumbers and restaurants, but if you want to refine your results to, say, "takeout restaurants" the results were pretty weak.
Overall, I like it. I feel it improves the experience within the Facebook universe. Do I see myself ever using it as a search engine over a people/interest discovery engine, not anytime soon.