This is a bug with the current version of the fglrx graphics driver. There are two ways to solve it:

You can remove fglrx and use the built in driver instead. You can remove the fglrx driver in System Settings › Additional Drivers. Select the driver that is currently installed and click Deactivate. That might solve everything, depending on how well the built in driver supports your graphics card. It might feel a lot better in some cases, because it is much better integrated, but results are quite varied.

So, your other option is to manually upgrade to the latest version of the fglrx driver. This bug is (almost) fixed in version 12.1. Upgrading is explained on the Ubuntu Wiki:

First, download the latest drivers from http://support.amd.com/us/gpudownload/Pages/index.aspx
And remember where you have downloaded them

Open a terminal and type the following:

cd ${*Where you downloaded the driver*}

sudo apt-get update

sudo apt-get install libqtgui4

sudo sh amd-driver-installer-*.run --buildpkg Ubuntu/oneiric

sudo dpkg -i *.deb

sudo aticonfig --initial

In the step with amd-driver-installer-*, you might need to change that to the name of the file you downloaded.

And then restart your computer.

After you do that, you might find that Gnome Shell still runs quite slowly, even with the latest fglrx. If that is the case, you need to set something in an environment variable.

Open a terminal again, and type the following:

gedit ~/.profile

A text editor will appear, showing your .profile file. At the very bottom of the file, add a new line with the following:

export CLUTTER_VBLANK="none"

Now log out and log in again.