When I used the surface on a 1080p TV it tried to scale the video to 1360x768 (the native surface resolution) by default. My TV did not like this resolution and looked pretty terrible, scaling artifacts, etc. Also, the video lagged at stuttered.
Fortunately, The Surface RT doesn't act any different than a Windows 8 laptop in how it handles an HDMI connection. Windows RT sees it as a 2nd monitor. You can go into the display properties from the desktop and change how Windows handles the 2nd monitor. (I think the Win-P hotkey lets you toggle between the typical modes without dropping to the desktop). If you disable the built-in display and use only the HDMI, or if you change the HDMI to be a unique display and not just a clone of your primary display, it should look just fine on your TV.