Hi Peter,
Regarding your issue, it was caused by your mis-configuration of your Joomla user groups. Please see:
http://screencast.com/t/xvaxhA2V
http://screencast.com/t/R00tPrVUDB
You've configured all your Joomla user group ( even the public group ) to have the super admin access. Meaning to say, everyone in your site now is the super admin.
EasySocial do not allow a super admin to moderate another super admin thus you are not seeing the moderation tool.
I strongly advise you to re-adjust your permission on your Joomla user groups
Hope this help and have a nice day!