The most likely cause is that you are running Teamviewer (a wonderful easy-to-use remote control application).
The root of all your problems is called the QuickConnect button, and unless you customized you Teamviewer, it should be located next to you window Manipulation Buttons. The double-sided arrow can be used to instantly share a window with one of the partners in your list.
This also blocks Battlefield 3 from going full screen. Somewhere Frostbite (the Battlefield 3 engine) has taken a different route to that of normal developers, as this is only game I have come across that can’t go full screen because of teamviewer and also the only one that causes Windows to throw the annoying "Do you want to change the color scheme to improve performance?" pop-up. (See How to Disable "Do you want to change the color scheme to improve performance?" in Battlefield)
So here is the solution:
NOTE: This might not be the only solution. There might be several more out there, but this one worked for me.
NOTE 2: This might help for any game not being able to run fullscreen.
Enjoy Battlefield 3!!