Well, Connections does not conflict with itself/extensions/templates … not sure if that is what you’re saying. I run them all on this site as well as my dev site.
The fact that you’re having trouble working with menus indicate the issue is not being cause by Connections. I say this because now scripts or anything interacts with that admin page. Obviously there are widgets if you have the Widget Pack installed, but it does not load any scripts or anything on that page (version 2.0 will, when released). That too indicates something else is a miss.
But… have you tried deactivating all Connections plugins to see if the issue goes away or not? If you have not, that would be the first thing to try.