I am experiencing the same issues, so I just wanted to contribute my story in hopes that Apple will issue an official response the same way they did for the mid 2011 iMacs. With so many people experiencing this issue, it is not right for Apple to ask all of us for a $600 repair.
My screen glitches through out the day, but while frustratingit is thus far bearable. I hope it does not get as bad as some have reported. For me glitches happen at their worst after closing the laptop and reopening it. Often this results in a freeze - the screen glitches, the mouse sometimes work but everything is otherwise frozen - and I must perform a hard reboot.
This was an issue prior to Mavericks but it seems it happens far more often with Mavericks. Sometimes the glitches are localized to certain windows and momentarily leave by interacting with the window. When I have a secondary display, it glitches more than the primary but it happens whether or not I am using more than one display. It does not matter if the computer is running hot or cool, it can happen regardless of heat. It can happen if I am using programs such as Adobe PS, or if I am only running Safari.
I have tried various energy saving preferences, zapping PRAM, Killing troubled apps. All provide temporary resolution only to have the problem return with in hours or days.
So far the outlook isn't promising for us MBP '11 users. Several reports of people who went as far as replacing the motherboard for $600 only to have the issue reemerge. Other users reinstalling OS X, trying different OS all together, and still the problem presents itself. Some users even created a domain to document the issue - mbp2011.com - those who were offered a $600 repair thought it was so much they just abandoned the MBP and got a MacMini. Not good!
Apple, swapping the motherboard does not help. Reinstalling OS X does not help. Users reporting past firmware updates did not offer a solution. It isn't reasonable to ask so many customers so much money for a repair that can't seem to be fixed. Please stop charging for any repairs and find a new approach in fixing this issue.