Having a sliding reputation score, over the last x months, would show the user's current activity on Stack Overflow more correctly than the current system does, I think. One of the main reasons is that the size of the community using Stack Overflow is constantly changing, and your reputation is changing with it. What I mean by that is that if there are only ten people using Stack Overflow, it is not too hard to be the first one to answer a question. With 100,000 users, it gets harder, and that indirectly affects your reputation.
Of course the total score should be kept as well, and that could be used to give access to new actions like today's reputation does.
UPDATE: The main goal of having some kind of sliding reputation will be to show how current the knowledge of the user is. Let's say we sit here looking at Stack Overflow in five or ten years. You will have a reputation based on answers you made five to ten years back. Is that reasonable? If Stack Overflow started ten years ago, mainly people who knew C (only an example language) or some other language very well would have a high reputation. A sliding window is something that I think would stimulate the community to keep up with their surroundings. If you're not up to date with the technologies/languages that are relevant, your knowledge becomes more and more irrelevant and your reputation should too, since I think it should reflect how valuable your knowledge is at the moment.