At its basic level, this idea was for a button which returns a page with a random tweet from the Favstar database. Without appropriate constraints, this could be a toss-up between finding hilarious, hundred-star tweets and "I like my mention so I starred it" single-star tweets.

Expanding upon that idea, a page of randomly selected tweets is even more fun, and even if there are sucky single-star tweets making the page, surely there will be some gold mixed in.

Even better yet, there could be a page allowing for some criteria to be applied to the random selection, say, only tweets with three or more stars, or 50+ stars, or under 100 stars, or only tweets without @mentions, or users not on the leaderboard, or users who give the same amount or more stars than they receive, or users with under X number of followers, etc. etc. etc. Such criteria, used properly, would foster community growth.

And one more idea before I stop bugging Tim =)
The idea has been presented already to design somewhat of an intelligent recommendation system for users & tweets within Favstar. This could mesh well with a random selection and/or random+search criteria, based on the types of tweets that a particular user tends to star.

Ok, I'll shut up now.
-Bock