I would install the latest beta drivers from AMD. I was having similar problems in Xbox Music and Chrome (artifacts and screen tearing). I installed 13.2 I believe and the problems went away. I believe it is due to idle clock speeds.
You can set idle clocks yourself, but I would exhaust the driver selection first. I have since moved to 13.3 with no problems.
You can test by booting up a program like Kombustor and then browsing to see if you still have the problem. If you don't have the problem when there is a load on the card, it is the idle clock speed.