I also have the Mid-2010 15" MacBook Pro and have been experiencing the graphics glitches since switching to Mavericks.
I have been to the Apple Store about four times in the last month:
1) We addressed possible hardware issues, replacing my logic board, all of my RAM, the bottom shell of my computer since the shell was dented, and the battery since that was also kind of failing. I restored from a backup, and 24 hours later, the issue returned.
2) We addressed more possible hardware fixes, replacing my logic board again as well as my display. I restored from a backup, and 24 hours later, the issue returned.
3) This time we decided to take a software approach. We cleared my Mac and did another clean install of Mavericks, and instead of doing a backup, individually redownloaded my applications from the app store and the Microsoft website for my Office apps. We also dragged over my music and libraries and documents. The problem came back in less than 24 hours this time.
4) I went back yesterday, and they decided to "partition" my laptop or something. Now I have two operating systems on my laptop that I switch between so I can use my iCloud with Pages for my papers and stuff. They wanted to see if the problems would recurr in Mountain Lion, so that is what I have been trying since last night.
The guy I had last night said that version 10.9.2 of Mavericks would come out soon but that he didn't think it was set to address any graphical issues. I'm pretty sure the issue will not occur in Mointain Lion since the problem started when I downloaded Mavericks. Mountain Lion seems a lot slower so far, and I don't really want to have to restart my computer all the time to switch operating systems, but it is what it is. We will see what happens.