How to remove icons/shortcuts from Unity menu?
It seems that you can't remove apps from the Dash, however you can manage your launchers (*.desktop files) in one of the following directories:
/usr/share/applications
/usr/local/share/applications
~/.local/share/applications
If your launcher file is in any of the first two directories, you will require root permissions to remove it.
I use an application called alacarte (atalacarte is a program that for editing freedesktop.org complient menus). It allows you to remove the unwanted launchers from the menu or create/add new ones. I had to install this app myself (apt-get) in Ubuntu 12.04. IMO this app should be part of a default Ubuntu installation.
I had the same trouble with deleting Firefox icon from Unity launcher. I installed two exemplars of Firefox: one with apt-get and one with dpkg from *.deb, so after removing both copies of Firefox, icon is still showed in Unity launcher.
Here is recipe that helped me:
Looking a package in dpkg
dpkg --list | grep firefox
result
ii firefox-mozilla-build:i386 35.0.1-0ubuntu1 Mozilla Firefox, official Mozilla build, packaged for Ubuntu by the Ubuntuzilla project.
Found! Well, when we know the name of the package, we can remove its remnants
sudo dpkg -r firefox-mozilla-build:i386
That's all, excess icon vanished from the launcher.