I'd like to argue for using OS native tools for this.
For example, depending on the flavor of Windows, Start -> Run or Start -> Search Box, -> charmap (aka Character Mapper)
It's more feature rich than what is in the XUL now, but does have to work through the clipboard.
For Mac OS X, System Preferences -> Keyboard -> Show Keyboard & Character Viewer in menu bar; then use Show Character Viewer from said menu.
I'd like to argue for using OS native tools for this.
For example, depending on the flavor of Windows, Start -> Run or Start -> Search Box, -> charmap (aka Character Mapper)
It's more feature rich than what is in the XUL now, but does have to work through the clipboard.
For Mac OS X, System Preferences -> Keyboard -> Show Keyboard & Character Viewer in menu bar; then use Show Character Viewer from said menu.