I'm running OS X 10.8.2, and I keep my calendars on Google for historical reasons, though the following problem is causing me think I should change. When I get an invite for an event, it shows in Apple Calendar as a gray box with dashed outline. I open it and choose Accept. When I go to the Google Calendar website it shows as accepted. However, in Apple Calendar I get an error, and when I clear the error by clicking Revert to Server or Ignore, the event is still gray. I had this problem on my old machine as well, which was running OS X 10.6.x, so it's not a new problem.
Suggest everyone check the default calendars on their macs, and iOS devices - the calendar in my iPhone was hijacking the calendar invitations. The default calendar should be the same in all devices. Hope this helps