Are you having issues on all browsers, Schweino? Firefox and Safari for our CF7 (updated to latest version) seem to be experiencing the issues you are describing. They work fine until you upload files, then the spinning never ending. However, not seeing any issues with Chrome, IE, or Edge. I haven’t had a lot of time to investigate, but will post any findings here.
That error you describe though, looks like you are using the default folder for files to be uploaded to. I believe the default permissions for wpcf7_uploads are Read only – 0755. I would recommend creating a new folder and giving permissions 0766.
If you do that you need to alter your wp-config.php
define( ‘WPCF7_UPLOADS_TMP_DIR’, ‘wp-content/uploads/yourfoldername‘ );
Hope that helps!
-james