Apart from the obvious one of actually responding in the first place, I have a mild beef with the way some site owners deal with debate in an comments thread on their blogs. I count three different ways of dealing with a comment thread:
I'm of the firm opinion that (1) is the best option. It has the (for me) huge advantage that you can get notified of new comments on the thread using a comment tracker like co.mments.com, and allows your commenter to make his points in his own way. The disadvantage is that threads can sometimes get a bit difficult to follow, particularly if they are long and complex. This is, however, the approach adopted by most site owners.
(2) Adding responses to the end of comments is also fine - it makes the thread rather easier to follow but you may not know if your comment has been responded to. Tim Worstall is probably the best known exponent of this approach.
You might make a case that (3) - interspersing responses throughout the comment - has certain advantages, in that the site owner can respond to each point made by the commenter. However I think its use should be discouraged, because it becomes something akin to a fisking of the commenter. It seems to me that a polite welcome to a commenter involves letting them say their piece, allowing other readers to appreciate the their argument in the best light possible. Interspersing ones own responses seems to me to be just plain bad manners - it's the equivalent of interrupting them at the end of every sentence. I know of two sites that use this approach - Real Climate and William Connelly (who is, coincidentally a Real Climate contributor). Are there any others?