Fixing dead/stuck pixels on Apple Cinema Display
You can sometimes fix stuck pixels by running something like this:

http://www.flexcode.org/lcd2.html

Hit the fix my screen button and it can attempt to unstick the pixel.  If that doesn't work then the best things that you can do is to make an appointment at your local Apple Store Genius Bar:

http://www.apple.com/retail/geniusbar/

and have the Geniuses look at it.  If it is under warranty still and it falls with in Apple's Guidelines for Pixel/Screen Replacement, they can replace the screen for you for free.  

If it isn't under warranty there will be a parts and labor charge, but they will let you know this up front and you can decide if you want to go through with it.  That is one of the great things about Apple, free diagnostics even if you don't go through with the repair.  So technically you don't have anything to lose.  (Except your time, technically)