This issue was fixed for me when I edited the wpdm-functions.php. The directory depends on your setup.
For me it was /opt/bitnami/apps/wordpress/htdocs/wp-content/plugins/download-manager/wpdm-functions.php
Line in question was using an object method instead of an array reference. After updating this my ReCaptcha problems went away ??
Line 267 can be changed to:
$ret = json_decode($ret['body']);
Hopefully the developer can update the code for another update if possible.
