Useful post, thanks!

Since some folks might prefer using the "Official" button style, I figured I'd create a small "child plugin" to extend Jetpack's sharing functions and add a new ManageWP.org sharing button. The plugin will use ManageWP's button with the counter or the text button depending on your Jetpack sharing settings.
http://wordpress.org/plugins/mwp-sharing-jetpack/

Then click on the create share button. This is where it becomes confusing. After clicking the create share button, you’ll see a spinning circle indicating that something is happening. When it stops, the add new service pop-up stays on the screen. This gives the appearance that it is broken or something is hanging, preventing the button from being created.

That's interesting. I couldn't reproduce the issue on my end; the pop up disappeared and the new button appeared in the list of available services.
Do you experience similar issues when creating Publicize connections, on that same page?