I found a solution for this at http://oguzarduc.blogspot.de/2012/08/applescript-for-activating-airplay.html

This script activates AirPlay mirroring on OS X Mountain Lion 10.8:

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tell application "System Preferences" 
set current pane to pane "com.apple.preference.displays" 
activate 
end tell

tell application "System Events" 
tell process "System Preferences" 
click pop up button 1 of window 1 
click menu item 2 of menu 1 of pop up button 1 of window 1 
end tell 
end tell

tell application "System Preferences" 
quit 
end tell

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Now I can hit the button on my BT remote while sitting in the living room and having my mac mirrored to the TV.