Same issue here. site http://www.mediame.tk as a multisite installation. Having issues with main site, /thinkparadox/ and /journalofparadox/. Issue started immediately after updating Jetpack this morning.
My attempts to resolve the issue in case it was a faulty install was as follows:
Completely remove plugin itself as well as all mentions of it from the database especially in wp_options (my tables are different, for security purposes, but still).
Redownloaded and installed a fresh copy of Jetpack. Plugin activates fine, even as a network activation without a hitch, it's connecting Jetpack to WordPress.com that the error pops up.
Errors the same as OP. Figured it might have been the BuddyPress XML RPC plugin causing issue since I use that with BuddyDroid on Android. Disabled it, still not dice. Not sure what other path to take at the moment.
Also worth noting is that I don't have any caching plugins activated even though DB Cache Fix is installed. My server runs with Apache, Nginx and Varnish.