I like this idea or Something Like This™. The intent was explicitly to give higher rep users a way to bring attention to questions [on stack overflow] which either have gray area or truly need further refinement. This wasn't so much for new guy A asks question and new guy B answers obviously wrong answer to old guy C but new guy A accepts new guy B's answer being so happy that his question received an answer on the internet! type situations, but more for high rep users to use that rep to challenge some of the harder questions. The mechanics are just thoughts, and sitting here now I can think of 10 awesome implementations of Something Like This™. It's also fun to watch people with more reputation defend points made.
WE'RE ALL GAMING IT SOMEHOW
Maybe gaming it isn't the right word, but just about every consistent answerer has a pattern or methodology to how they select questions to answer. Personally (though my answer rate has dropped off significantly since my relocation), I scroll to the bottom of the interesting page, find a non selected answer question that's 3 or 4 hours old with only 2 or fewer answers, and research the solution to it. I also browse a few select tags and spend a fair amount of time reviewing each question posted to them, answered or not.
Integrating a more directly localized competitive mechanic would be something I for one would see as engaging. The community gets the benefit by means of me answering harder questions with more detail and research.
PROBLEMS WITH CURRENT SOLUTIONS
Editing someone else's answer for reasons other than making it more readable or to fix an obvious typo kinda gives me the willies. If a better answer exists, it should be it's own answer because then the person with the better answer gets the reputation for it, and the person who answered it initially doesn't get reputation undeserved by ability. Of course sometimes answers just need a little help and adding a comment works fine.
If the question is old and/or has a selected answer, the likelihood of a new answer gaining clout is particularly low because unless the reader is well studied enough in the topic of the question to know the selected answer is immediately wrong, they should or are completely justified in just accepting it themselves and moving on. If the selected answer appears to solve the problem, my time is better spent doing things other than running around questioning everything because otherwise I would never get anything done.
Creating a bounty is useful, though I would almost prefer no check mark show up on the selected answer until the bounty is completed and the question is returned to larger pool.
In talking with some other team members about this later on, it became clear that a few requirements have to be in place, and for the purpose of not bastardizing what all was said, I'll just stick to the themes.
OVER TIME THE COMMUNITY SELECTED ANSWER SHOULD BECOME THE CORRECT ANSWER
The idea here is two fold. Over time the correct answer to some questions does in fact change, either as new issues come to light or frameworks are updated or whatever. The other is that over time the answer with the most upvotes helped the most people, even if it is not the selected answer. "Duels" do not directly address this problem, but are just instead one mechanic that addresses it as most of the existing mechanics do. There are a few good ideas out there on how to handle this more directly.
PEOPLE DON'T LIKE LOSING REP
I would have to conjure up some data explorer queries to show to what extent this is true, but I am confident in saying this affects a large portion of the community. As stated earlier, the mechanics are open for discussion and perhaps there is a better way, but on that note, I think it makes the concept more interesting to have something on the line.
WOULD THIS MAKE THE INTERNET BETTER?
I say yes. Gray area questions have a lot of value because they often involve situational factors or long foresighted effects which many people have never experienced or thought of. Some kind of dueling mechanism would get multiple higher rep people involved in answering these tougher questions and bring more eyes to this useful information, which is essentially the definition of making the internet better. These questions would also really appeal to people who have a more answer and defend than answer and move on mentality.
STACK OVERFLOW ISN'T A PLACE FOR DISCUSSION
While true, there are a number of valid questions on SO where some discussion is warranted because multiple solutions are possible, all of which would be valid answers and all of which have pros and cons which need to be weighed against the situation at hand. Lets take for example a question of mine about constant declarations in c#. If my question had instead been "I am writing my own language and trying to implement a constant keyword, should I allow a static modifier on it?" then you could read through the discussion on my linked question to see how there could be multiple legitimate answers.
I'm always thinking about the Careers site. I can't help it, it's what I do and everything I hear about I want to know how it fits into the Careers site. From a Careers standpoint, being able to adequately defend a position on a development team is an important thing to know about someone, and linking successful "duel" questions or a dueling score card on your Careers profile would be an interesting addition and have the possibility of giving employers a way to gauge how a candidate might interact with the team while discussing design or implementation details. (Or possible features such as this! wowza!)
Tangentially, an alternative mechanic might be that once you receive so much rep in a tag, you can enter challenges of some sort that last for X days, can have up to Y people competing at once and everyone answers questions tag Z. Whoever gets the most rep for that tag in that amount of time get a mark of distinction.