When I add new comments to a WordPress post on the WordPress side, two identical comments now appear under the post in WordPress. I believe this is due to SP 5.5.5, as updating to that is the last change I made and the double-comments did not happen before. I have my WordPress posts linked to the forum to make comments display in both places.
Also, as you can see on this page, if a comment is held for moderation and then approved (as with the first comment by Jazyk), there are also two identical comments — but one of them is dated according to when it first went in the moderation queue, and the other is dated according to when it was approved.
http://www.waywordradio.org/le-petite-voyage/#comment-3170
Adding new comments on the forum side does not make duplicate comments on the WordPress side.
Disabling Simple:Press doesn’t allow me to test as there are no comments at all displayed if I do that.