It looks as though you might have a corrupt installation. Try renaming or deleting your personal configuration folder. Details of where to find it are in http://forums.adobe.com/thread/494812. After deleting or renaming the configuration folder, relaunch Dreamweaver, and see if that makes a difference.
If it doesn't cure the problem, uninstall Dreamweaver (select the option to remove preferences), and reinstall.
If that doesn't fix it, you'll need to contact Adobe technical support.
I have this exact same problem, also running CS6 on Mac OSX 10.8.2. If you click where the UI elements should be, they appear. Other than the servers panel, everything else in Dreamweaver behaves normally. Another system still running Lion does not do this.
Do you have the latest update for DW CS6?
Nancy... see the OP's screenshot above. The UI elements for adding a site are missing. On my system, they will appear only if you click in the general area where they should be. This is most certainly a bug.
Nancy O. Thanks for your posts. I have been trying to remedy this issue all night. I am running a more recent version than tygra & Mike_Pringle, version 12.2 Build 6006, as far as I know that is the most current cloud installation. I am going to take David Powers tip and do a clean reinstall and see what happens. Will let you guys know ASAP. Weird quirk this one is. Harmless but annoying.