How can instantiated classes access the Document class?
Even after I name the Document class using the Properties bar in Flash, att
The document class is not inherently a globally accessible object. If you want to call methods that are in the document class, you'll always have to pass a reference from Main to any other classes/objects that want to call its methods. A more object oriented approach would be to dispatch events from your other classes (Other) for the Main class to listen to and call an appropriate method in itself.
If you are unconcerned about keeping a good OOP structure and want to access the document class from a display object that has been added to the display list you could try something like: stage.getChildAt( 0 );