Should I post a response to reviewers online?
You are free to post your response as you see fit, If you know who the reviewer(s) is/are then you may need to think twice about mentioning their name(s) since. I am not sure how you may be thinking of posting such comments but I assume you will rewrite them into some form of self-contained text. As such it would not be very different from a blog entry and so one suggestion would be to use a blog type web to add comments around your publications. You may also provide means for commenting on your papers and associated posts.

But, in short, no problem posting your own thoughts but stay clear of adding the thoughts of others that may be given in a context other than open posts.