If you spend enough time blogging it is guaranteed that you will witness disagreements between bloggers and or commenters. And as you already know or soon will see arguments within the online world can become far nastier than they do in person and in much less time.
Some of that is due to misunderstandings that are innocent in nature. In cyberspace there are no verbal clues or facial expressions that you can use to help interpret what is being said. Humor and sarcasm can easily be seen as being something else.
And of course there is the ever present issue of people taking advantage of anonymity to say things that they might not otherwise say to you, especially in person.
If you are a blogger you will want to decide what sort of comment section you are going to have. It is up to you to set the tone and create an environment. So it is your choice as to whether you let the comment section turn into a giant free for all or if you try to maintain a sense of decorum.
This leads to one of the ongoing debates within the blogosphere which is whether there is merit to engaging in arguments with others. Many people think that it serves no purpose. They'll tell you that you never change anyones mind and that the end result is that you end up irritated and angry.
I have to admit that I rather enjoy these little sparring sessions, but in general I try to avoid them with a few exceptions. The primary exception occurs when gross misinformation is being passed off as truth in which case I have no problem wading into the fray.
As a rule of thumb I don't expect to convince those screaming loudest within the comment sections. Rather I am interested in influencing the lurkers. It is the readers who say nothing but follow along that I am trying to reach. Primarily because I suspect that they will be more likely to have adopted a position of neutrality.
It might be wrong, who knows. But to me it seems logical and it offers the biggest bang for the buck.