HERE. From this blog entry, the writer has provided a 'wrapper'/launcher application that allows you to open the AirPort Utility 5.6.1 successfully. I have successfully validated this works as of today and thought it would be worthwhile to share. The below post is for historical purposed only.
If you need to access/manage an older Airport devices (in my case the Airport Express), the built-in Airport Utility in Mountain Lion cannot access the device. I know, dumb, huh? Well after scouring the web, I found a solution - you need to install an older version of the Airport Utility (5.6.x specifically). The below steps were originally taken from this Apple discussion thread: https://discussions.apple.com/thread/4172563?tstart=0. I updated/revised it to clarify a few of the steps needed.
1. Download the Airport Utility 5.6.1 disk image at http://support.apple.com/kb/DL1536.
2. Double-click and mount the disk image. Drag the install package (AirPortUtility.pkg) to your desktop.
3. Open up the Terminal application (Go > Utilities > Terminal.app).
4. In the Terminal application, make a temporary directory and cd into it: mkdir tmp ; cd tmp
5. Extract the Payload file from the install package with xar. Here's the command to type into Terminal.app: xar -x -f ~/Desktop/AirPortUtility.pkg Payload. The result will be a directory named AirPortUtility.pkg (just like the file, but now you can move into it to get the files you want). Inside will be a file called Payload that is a compressed archive of AirPort Utility.app.
6. Extract the app. Here's the command: gzcat AirPortUtility.pkg/Payload | tar -xf -
7. When it finishes there will be three new folders Applications, Library, and System. (The copy of AirPort Utility 5.6.1 will be in the Applications >Utilities folder) Type ls to list the directories if your curious to check it out.
8. Use Finder (Go > Go to Folder and type in ~/tmp) to rename Airport Utility to Airport Utility 5.6.1 (assuming you want to keep version 6 as well) then drag it to your Applications > Utilities folder.
9. The final step is to launch AirPort Utility and confirm that it works. You'll probably want to go into preferences and turn off the option to check for updates.
10. If all is good you can remove the temporary directory: cd .. ; rm -rf tmp (or drag it into the trash with Finder).
Hope this helps someone out like it did for me!