I get a pink and red error box when I try to upload images using the Add Media button from the add post screen. Error says "An error occurred in the upload. Please try again later." I get the error whether trying to upload a new image or designate a featured image.
I can add media via the media library. Then copy the URL from there and manually insert it in the post. Major pain.
I have scoured the WP forums and have found no solution to the problem, other than being told to disable all of my plugins (which I did; didn't help) and switch to the 2012 theme (SRSLY? after all the time and money I've spent developing my theme?)
I have tried to add a "me too" comment to the other threads that discuss this problem and was told by the admin to start a new topic. WordPress continues to claim it's not a WP problem. I am very frustrated and hope that if enough people complain WP will develop a patch for 3.6 that resolves this problem.