How to stop Alt from triggering Global Menu?

You can go into Settings > Keyboard and change the shortcut or disable the shortcut there

I also use Emacs, but with the GUI (emacs & in a terminal shell) I don't see this problem - Alt-H selects the whole buffer.

When I run Emacs specifically inside a terminal (emacs -nw) I see the problem as you report. The Alt key is intercepted by the terminal application.

If you really want to use text-mode Emacs inside a terminal, you should use the terminal's menu (click inside the terminal window, then go to top of screen), then select Edit > Keyboard Shortcuts..., and uncheck "Enable menu access keys". After doing that, text-mode Emacs treats Alt-H just like GUI Emacs.

(edit) to disable the Alt key in all applications, run ccsm (CompizConfig Settings Manager), select Desktop -> Ubuntu Unity Plugin and disable the "Key to show the menu bar while pressed" and possibly "Key to show the HUD when tapped" too.

You may need to install ccsm using sudo apt-get install CompizConfig-Settings-Manager.