I did restart the computer but that had no affect. So, I decided to reload everything after downloading XQuartz and Inkscape again. This time, no problem but I think it had to do with the fact that Inkscape starts the XQuartz server and if it seems that if XQuartz is running already then that is why...

I also just updated to Mountain Lion and installed the latest version of XQuartz (ver. 2.7.2). I also downloaded Inkscape and installed but it fails to run. The program starts up, the icon briefly appears on the dock and then disappears. I checked the Console Log for the Mac and I see only a message...