Okay, here’s a quick workaround until the bug has been resolved:
In the admin panel where the field groups and fields are defined, you have to set the preview image of each image field to “thumbnail”. After that, the upload/selection of an image won’t fail anymore. Except the uploaded image is even smaller than 150×150 pixels (the standard size of the WordPress thumbnails).
As long as it’s larger than that, you’re fine.