Realistic answer: I would quickly go insane attempting to deal with all of the dissidents a world leader would cause, in addition to all of the responsibility inherent to such a position.
Idealistic answer: If the world is under a single leader, the unity required for such an action would effectively mean and end to war. Should this occur, the need for a defense budget drops considerably. Obviously, there is still a need for a self-defense force in the event of uprisings, but that would be far less than a full military. Cutting this program would drastically reduce the necessary budget needed to maintain a government, so more money would remain in the hands of the people (more specifically, the ultra-rich). While I have absolutely no love for the ultra-rich, the amount of money we literally throw away keeping up with the arms race is ridiculous.
Other goals would be health-motivated restrictions on the industries, such as tight restrictions on the inclusion of trans fats within foods, and shutting down, rather than fining, facilities that break emissions laws.
So called "legislated morality" laws would be drastically cut back. If an action does not hurt anyone else, it should not be illegal, and a self-imposed moral system is far more important than a government making those decisions for you.
Fun answer: I would fund a "rent-a-friend" program (as featured on the cartoon Tiny Toon Adventures, but expanded to cover all age groups), so that hopeless introverts like myself can at least experience an emulated version of genuine friendship.