Given that the scores seem to be given in order's of 5's and 10's with the odd 2's, sitting on 666 seems likely rare. A badge for this would be interesting.
The point of badges is to reward behavior we want to encourage. Giving badges for getting a precise rep display for a bit doesn't really reward anything, it just gives people with 667 rep a reason to downvote a random post.
Just take a screenshot of your milestones.