Hi Ann-Marie,
I noticed that the PLUGIN through its auto scrolling feature somewhat affects the Ajax coding for the drag and drop, so perhaps look at any other Plugin that you may have installed that has auto scrolling or stock ticker type of news installed.
Lastly do this: select all the Plugins and do a BULK Deactivate and Open a NEW Tab window to test the drag and drop, then Activate each Plugin one by one while refreshing the Menus window.
This way for sure you will find the Plugin that is affecting your Menus, please post your results since this seems to be a common problem with a few Plugins.
Thanks!
-im