The preferred way of reporting MonoDevelop bugs is using the Unity bug reporter (Help -> Report a Bug from the Unity editor).
Alternatively, non-Unity-specific MD bugs may also be reported at http://bugzilla.novell.com (it will ask you to create an account).
When you report a bug, please be specific about what's not working correctly. I.e., what behavior you expect from the text selection, and what the actual behavior is.
To get the Assembly Browser window to work in MonoDevelop you need to tell it where to find the Unity and Mono assemblies. Go to Tools > Options > Build and then select the Assembly Folders tab. On my Windows 7 installation it was sufficient to add these two paths: