I have the same problem on all our sites. In our case, we are using SSL and we have found that the plugin is using http instead of https when loading the content of the popup ([oursiteurl]/nextgen-attach_to_post), which is then blocked by the browser as insecure.
Is there anything I can do to make it load over https? I made sure the site has the right URLs in the General settings, but there was no change. I am willing to modify the code, if need be.