If you use the JetPack Plugin "Publicize" to generate Tweet or Facebook update from a post when it's published, you can NOT use "Duplicate Post" to clone a new post from an old one because the "Publicize" feature will be grayed out and WILL NOT WORK on the new post.
Jetpack support suggests the problem is:
"The plugin seems to duplicate the content, but also the Post Status. This will indeed cause Publicize to stop working, because it will be disabled when a post has a 'Published' status."
I hope the developer of "Duplicate Post" will fix this flaw because it's an awesome plug-in otherwise!!