Used to work perfectly, until WP upgrade to 3.9

The plugin worked perfectly, until I upgraded my WP to 3.9.
Image uploading never was that easy.
But now it is broken. I could not find interference with other plugins. There are no javascript errors reported by the browser (Firefox and IE). No PHP errors in the server logs. No clue why it does not work. That’s a pity. I would offer to help debugging, as I see more reports of problems with the plugin for WP 3.9.