I purchased MJ Basic, installed it over my 1.2.7 from last year and then it breaks my layout...not happy about that, but I'll work on it. 

The real mystery is why after upgrading it takes 5-7 seconds to navigate back to the Joomla control panel page. In the status bar, it reads:

Waiting for www.mobilejoomla.com...

I noticed the MJ site was rather slow today, is that why? And why is it reaching out to MJ's site at all?

It was fixed in MJ 1.2.9 (this version uses asynchronous check for updates).

Thank you for your response! I am running 1.2.9 and it is still very slow. Should I re-install?

As a temporary solution you can disable Mobile Joomla! CPanel Icon plugin.
I've just committed patch
github.com/mobilejoomla/mobilejoomla/commit/21cf49afef48563af2d18779b7028ca4b152933a
that should fix the issue in next MJ release.

Thank you, the temporary solution will work for now. Is this problem causing the mobile pages to load slowly as well? I have noticed that on the live server they are a little sluggish as well.

No, it's backend only.