I noticed an issue on posts where they were showing as insecure when I was browsing via https. I tracked it down to the mappress plugin. I upgraded to the latest one but the issue is still there. Can you confirm if it is likely to be the custom marker I am using. It is in the uploads / mappress folder. The style sheet is https so seems ok.
For now, you could try the ‘upload_dir’ filter (from WordPress file wp-includes\functions.php) to change the result of the wp_upload_dir() function. I haven’t tested it, but something like this might work (add it to your functions.php file):