Adding Disqus removed the comment spam in one go.  Unfortunately the side effect is that I’m getting trackback spam.  Which is just as bad.  It all goes to moderation, and akismet is now switched on to deal with the dregs.

It seems that the ping/trackback settings can be hidden under the All Posts->Screen Options.  Once they are shown, you can additionally just switch of the ping/trackbacks via a bulk edit of all the posts.