My resolution is stuck at 1280x720 when connected through the Moonlight Streaming Client.

Open Screen Resolution by clicking the Start button , clicking Control Panel, and then, under Appearance and Personalization, clicking Adjust screen resolution and choose screen 2

7 days later

Are you connected with the panels control client? You have to turn off the console in the panel in order for screens to switch back to full resolution. Soon as you connect to console within the maximum settings control panel, it will reset resolution back to 720p.