[Mojo]

I tried rebuilding the Launch Services database but the problem was not fixed.

I contacted Apple tech support this morning. The fellow who helped me had used SuperDuper! in the past so he was familiar with the utility.

We ascertained that the problem occurs only when the external drive is powered-on and connected to the Mac Mini at startup. (It might happen if I power-on the external drive after booting the computer and check for updates, but I haven't tested it...) It doesn't matter if the apps on the external drive are current versions; the App Store indicates that they need to be updated. (But this morning the App Store showed an app that needed to be updated while the button was grayed-out with the word "installed." Curious!)

The tech rep told me that we could elevate the issue to a senior tech support rep but he didn't think that it would provide us with a fix. When he spoke with that department while I was on hold he was told that they didn't have a fix. And since Apple considers Time Machine to be the approved method for backing-up data, they don't consider this to be a Mountain Lion "bug." So I shouldn't hold my breath waiting for it to be addressed in a future update. They will make a note of the problem but it is not a priority for a fix as far as Apple is concerned.

There certainly seems to be a glitch somewhere with Apple's software, since this has never happened to me in the past. But Apple doesn't seem to be inclined to deal with it even if other people report having the same problem.