Personally I think it's a great idea to respond to other answers in your answer, but I'm pretty sure I'm going to be in the minority on this one.
Why? Well, the main reason is because often people don't read the comments to see if there are counter arguments to an incorrect answer. Heck, sometimes the system hides comments for us... So putting a specific refutation in another answer (in my mind) is a perfectly legitimate way to overcome this shortcoming.
That being said, I wouldn't be a fan of simply having the refutation as the entire answer. I think if you are going to refute someone else in your own answer, you'd better have an answer as well. Something that is only a refutation should be left as a comment (despite all the afore mentioned difficulties with that system.)
I have offered other, far cleaner, solutions before. But as you can see from clicking the link, there's a lot of hatred towards that particular solution. Pity, because it's the most obvious thing to do if you ask me. (Read the whole post if you want all of my thoughts on why the current system of upvotes and downvotes has some flaws...)