Able to have anonymous users read your blog, but anonymous users can't post a comment? If so, here is how we fixed our Implementing SharePoint blog (we were wondering why no one had any comments….).
First you will need to ensure that anonymous access is turned on for the site (if anonymous users can see the site, this is not your problem, but it will be good for you to check). This is done by going to the Site Settings for the site. Select Advanced permissions under the User and Permissions settings. On the Permissions page, select Settings | Anonymous Access and ensure that Entire Web site is selected for the Anonymous users can access setting.
To enable comments from anonymous users, you will need to open up the permissions on the Comments list that supports the Posts list. Open the list settings for the Comments list and select Permissions for this list under the Permissions and Management section. At this point the list is inheriting the permissions from its parent web site. You will need to create unique permissions for this list. This is done by selecting Actions | Edit Permissions. Select OK for the "You are about to create unique permissions for this list. Changes made to the parent site permissions will no longer affect this list." dialog. You will note that several other options appear for managing permissions. Select Settings | Anonymous Access and add the Add Items permission for the Anonymous user (note that View Items should also be checked).
Now that you have set it up properly, you will need to logout of your blog site and then open back up as an anonymous user to test your settings. You should now see the ability for anonymous users to add a comment to a blog post. Since our comments are fixed, I am expecting several wise "comments" to this post…