Besides the currently known problems with commenting, which involve the post template and various local computer settings, there are some odd details that not everybody is aware of. If you have a private blog, you'll face a lesser known challenge with comments.
If you are in the habit of restricting the ability to comment, in your blogs, to members only, you may want to change that policy, when setting up a private blog.
Setting "Who Can Comment?" to "Only members of this blog" will leave your Designated Readers unable to comment.
That's not good!
When we setup permissions, we're told that the blog membership list, which includes Administrator, Authors, and Readers, is limited to 100 entries. There, "Readers" are implied to be "Members". In this example, we see that "Readers" are apparently not "Members".
I'll explore this oddity further, in Private Blogs And Designated Readers. It's possible that this is an intentional decision, to give blog owners an additional level of control.
(Update 2015/06/24): Blogger has reduced the confusion, by eliminating non authenticated ("guest") access, to private blogs. All private blog access will require Blogger authentication.