Duplicated Icons in Applications directory from dock.

Are you telling me that the presence of DataRescue is causing it? That is, do you recommended removing it?

This whole episode just brings up one of my chief annoyances with the state of software today: the lack of programs that will analyze state (i.e. retained data) for validity, especially in relation to others. For example, it's a fairly common optimization to have precomputed values (not just cache) that depends on other data. If those get out of sync, all sorts of strange things can happen. It's perfectly feasible for people to write programs to check for consistency, but this gets short shrift. This is why the "sledgehammer" - doing a factory reset, etc. etc. often works. But heavy handed doesn't begin to describe it.

I haven't run the recovery for quite a while, so it was definitely pre-Tahoe. Here's another interesting fact: before Tahoe I had always had significant problems with Spotlight and the Apps folder in the dock. For spotlight, if I would try to search for an app it would just hang up (many minutes without finding anything). I tried rebuilding the spotlight index many times, but it didn't change anything. When I would click on the Apps folder in the dock, it would often take a minute or two to populate the icons there, which I found strange. After installing Tahoe all of this got fixed. I would expect that in order to populate the Apps icons it just needs to search the directories:

/Applications, /System/Applications and ~/Applications, which should be almost instantaneous.

I ran Etrecheck and looked at the full report. It made no mention of spotlight.

I just checked. I searched the only external drive that isn't dedicated to Time Machine backups. There are no '.app' directories there.

I just checked. It looks like all of the apps that have duplicated icons are the ones in /System/Applications.

It doesn't. That was the first thing that I tried. I think that that indicates that something else is broken.