@rock.lee. I’m trying to fix my upload issue for the whole weekend now. I’m happy to read your comment!
In my function.php I call a php file where I register my custom posts. In that php file I indeed had some HTML mark up (<!– Some text –>). After I deleted the HTML mark up from the php files Everything worked again.
So for everyone else: I could be that your theme uses custom posts and that there is HTML mark up in those files.