It would be pretty neat to be able to see your overlap between circles as a big venn diagram or something of the like. I keep finding out that I have handfuls of mutual friends with people I didn't know shared any of my friends (does that make sense?).
All a Venn (well, Euler, really) diagram would do is show you friends common between circles. I agree that building the graph and finding mutual friends would be nice, though. I generally just go to Facebook and look at our mutual friends, and I'm sometimes surprised, but it would be nice to have a tool that did it automatically.
I wonder if the API has a "mutual friends" call, you could write that pretty easily if so.