The next version of arcgis desktop (10.1) will have improved support for reading web maps. Any data stored in the map (like shapefiles and csvs) will become feature layers that later can be exported.
I will point out, however, that community editing is only really supported for data that you've created a service from. Either you have ArcGIS Server and you publish a feature service yourself, or you have purchased a subscription to ArcGIS Online (coming next year) that will allow you to create a hosted service from your data.
Data uploaded and stored in the web map can only be edited by the map owner. There is really no way for another person to make an edit and save it back to your map because they don't have write access to it. Now, they can make and edit and save it as their own map...
Thanks,
Mike