I'm having the same problem: running 3.5, tried disabling all plugins and reenabling them one at a time, and Jetpack appears to be the only one that keeps parts of the admin interface from working. I get the following error in the console when I load the post/page editor:
TypeError: e.widget.extend is not a function
and when I try clicking some of the buttons, like the edit permalink button, I see:
TypeError: editPermalink is not a function
My guess is that something is interfering with the interface buttons that make Ajax calls (for example, the get shortlink button works fine because it pops up an alert). The first error, at least, seems to be a jQuery UI problem.
Next I tried deactivating individual Jetpack components, and as far as I can tell the shortcode embeds feature is to blame—deactivate it and the problem goes away, letting me use the full editor interface as normal again. I don't use those shortcodes on my site so leaving that disabled isn't a problem for me, but for other people I guess it can serve as a temporary fix until the issue is resolved properly.
Hope that information helps someone!