I would like to have the ability to take an users profile on StackOverflow and run a query to see our interactions in the past. Like if he (or she) comments on a question of mine, or I answered a question of theirs, that would show up in the cross section.
One use case for the cross section query is to help with the moderator voting that is currently in progress. Looking over the moderators nominees I recognize familiar names, but I honestly can't recall our interactions in the past or if those interactions were pleasant. Using the tool that I am proposing you could run a query against the nominee and see where in the past your paths have intersected.