I was advised to start my own thread on the above subject which seems to be troubling a few users.
On our team site at http://phasma2.com, after updating to WP 3.6 and Jetpack 2.4, my widget page on the dashboard disappeared almost entirely and what little showed on the page was unresponsive, even the help and screen setting default buttons.
After deactivating all plugins, nothing changed. Worse still Jetpack would show a 500 Error page every time I tried to deactivate it.
Before that though I changed to the Twenty Thirteen theme and other default WP themes to see if the incompatibility was with my template (Aggregate by Elegant themes). This did nothing to alleviate the problem either.
In the end I was forced to delete the plugin folder via FTP. This restored all my functions to normal.
The site uses Jetpack mainly for the good social sharing package and stats control that it contains. These two functions are pretty integral to the way I manage the site. So understandably I would like to be able to re-install Jetpack.
My Site is run on WP 3.6, always kept fully updated, my hosting service is on HUB Web hosting. Below is a list of all the plugins I have used in to date, and so far with older versions of Jetpack they have caused no issues to occur.
Easing Slider "Pro"
Ninja Pages, Categories, and Tags
No Right Click Images Plugin
Ultimate Tag Cloud Widget
Yet Another Related Posts Plugin
Addendum: I tried uploading an older version of Jetpack but this had the same result forcing me to delete this from my FTP too.