Mountain Lion displaying graphical artefacts on screen
Check for updates through the Mac App Store first just in case Apple may have fixed this (obviously not everyone is experiencing this issue, but they may have anyway).  In the comments of this article about Mountain Lion bugs, many users are expressing the same issue that you are having, and having to logout and back in again to fix this.  

Another thing you might try (if you haven't already) is to back up and re-install Mountain Lion.  

update Everyone on this thread has the same exact issue. Yes, it is a bug, and yes, the only workaround is to killall Dock. I suggest using an AppleScript with Login Items, launchd, or Lingon (old, free, unsupported version here, and $3 newer, supported version here) to run killall Dock as soon as you log in so that the Dock just restarts itself immediately.  Meanwhile, submit this bug to Apple.