Apple - Xcode update would not work, and now won't leave the App Store update queue

I was able to fix this problem by correcting the permissions for Xcode. Run this from your Terminal:

sudo pkgutil --repair com.apple.pkg.Xcode

It actually installed as I was doing this. Many of the permissions reported as "should be drwxrwxr-x , they are drwxr-xr-x".

I was having this exact same issue all night and wasted a good 3 hours troubleshooting it. I didn't have to go through all of the steps that the other answer provided, but my fix was simply deleting my existing XCode from /Applications using an app called AppZapper (the OS X equivalent of Revo Uninstaller for Windows).

AppZapper makes sure to delete all of the other files associated with the application you are trying to remove. You have to select a checkbox in the preferences in order to be able to delete Apple applications, but as soon as I zapped my existing XCode and emptied the Trash, the new XCode immediately started downloading from the Mac App Store.

Just managed to get it downloading by requesting the web version (https://itunes.apple.com/us/app/xcode/id497799835?ls=1&mt=12) of the app store to trigger an external request (press allow).

On that "page" in the app store (where you may see screenshots of xcode) a button should also state "Update". And pressing that update button worked - different than the button in the "Updates"-Section posted by OP.

Don't know why, but saved me a ton of time not having to remove everything and redownloading.