For the last few years I had (for some unknown reason) three entries for VLC in my "Open with" menu in the Finder. There was no way to remove them from VLC itself and I couldn't find a way to do it myself. Until today. The following steps are also valid for other application that have stale "Open With" entries in the Fidner on a Mac running MacOS (nee Mac OS X)
The first step is to close the offending application, just to make sure nothing is still open that could block our attempts). Then open a CLI terminal (Terminal, iTerm, etc) and go to "~/Library/Application Support/". You will find loads of qpplication related directories (maps, folders) here. Remove all the directories that have something to do with your application ("rm -rf VLC" etc).
The last step is to recreate the "Open With" menu and restart the Finder. This might take a few seconds ("/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user" and "killall Finder")