Updating / Upgrading Xcode to 6.0.1 does not work
Try deleting the Xcode.app from your /Applications folder and replacing it with the Xcode.app from inside the dmg that you downloaded. Once you have replaced the Xcode application try to open it and it should work. You usually can't run packages or applications from inside of a mounted dmg. It is recommended to copy what you need from the dmg and then running it.