MacOS – Why does finder report the applications are in the trash when I use Open With

This is a permissions effect. Most Application installed on Lion by default, via the App Store, and some installers are installed as system a.k.a Root and root only by default has Read and Write access to the Applications installed as root, while everyone else including your user is read only or custom for each Application. Applications that you drag and drop are owned by you, and you can delete them at will usually with out a password.

Verify in the Finder or Terminal what the permissions are on Apps that require a password to move to the trash, its likely that those Apps that are set to read only access for your current user are the ones asking for a password and a temporary privilege to delete something owned by the system.

In terminal try:

ls -la /Applications

This happens because the LaunchServices database gets corrupted.

To fix on Mountain Lion:

1. Open Terminal.app in the /Applications/Utilities/ folder.
2. run /System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -r -domain local -domain system -domain user
3. Restart

This command has changed over the years, but I just recently ran the above to fix the same issue on Mountain Lion. This hint on Mac OS X Hints covers the command for other Mac OS versions over the years.

If you don't like using the command line, the free tool Onyx also has an option under Maintenance -> Rebuild -> launchservices will work too.

As for how to stop it, I really haven't ever seen a way. I am not sure what actually causes it to corrupt other than I know it is very actively used.