At long last, Apple has added the ability to find duplicate songs in iTunes with the release of iTunes 11.0.1. The update also fixes an issue with iTunes Match and makes iTunes more responsive when searching large libraries.
Apple's patch notes:
This update to the new iTunes addresses an issue where new purchases in iCloud may not appear in your library if iTunes Match is turned on, makes iTunes more responsive when searching a large library, fixes a problem where the AirPlay button may not appear as expected, and adds the ability to display duplicate items within your library.
iTunes 11.0.1 is showing up in the Mac App Store, but with the patch notes for version 11.0. You can, however, update to version 11.0.1 using that mechanism.
The above notes came from Apple's Downloads site. The download link on that page takes you to the main iTunes download page, where were able to successfully download a standalone installer for version 11.0.1.
If you click through to the KnowledgeBase article from the Downloads site, you will (currently) be taken to the patch notes for version 11.0. This will likely be fixed Soon™, but users can get the update with the two methods noted above.
Note that iTunes for Windows 64 was also updated to version 11.0.1 with the same patch notes. Windows users can find the update through the Apple Updater utility in Safari or iTunes, or use the main iTunes download page.