Is there device that will extend the range of Bluetooth? We currently have a Mac Mini setup to control a board room, but we have problems with a magic mouse when it is on the other side of the room from the mac mini.
Yes. They're called "Bluetooth Extenders." I have never used one so I can't offer specific advice, but I did look into them once for a similar problem.
Here's the one I planned on buying. Note that I never did so this is not a recommendation, just a suggestion: http://www.amazon.com/Miccus-Home-RTX-Bluetooth-Transmitter/dp/B00713RSE0