Hi, all !
I have the same problem of duplicate icon after upgrading iMovie through the App Store.
I would hope there is a way to remove a single icon you don't want, without removing the application, but didn't find it.
The only thing that I found to "reset" the Launchpad is the following (thanks to TUAW) ...
Pay attention : doing this will also reset all customization made in Launchpad (groups, positions, ...)
- Launch Terminal
- Navigate to the Dock application support folder (cd ~/Library/Application\ Support/Dock)
- Open the folder (open .) and drag all the .db files to the trash
- Restart Dock (sudo killall Dock, followed by authentication)