Okay I think I know why I'm not getting any answers here and elsewhere: I'm using the (wired) Apple Aluminium Keyboard. The support for this keyboard seems to be completely messed up in Linux Lint 14 + MATE.
First off, I noticed this white edge is the same that appears when alt tabbing. A double edge appears when there is more than one window for the current application. Yet I don't have any window/application switching shortcuts set to the "é" or "2" key (the number 2 key on azerty keyboard).
So then, realizing that the keyboard shortcut may be mapped to another scan code... I removed my shortcut Mod4+@ (tilde key on my keyboard) which I used for "Move between windows of an application immediately"... and after restarting the session the DockbarX Super+2 started working again.
So basically on this Apple keyboard, I map something to the tilde key (@ # on my keyboard), and instead it was responding to the number 2 key (é 2).
At other times I mapped Mod4+Q to emulate OSX's quit application, it would work for a little while, and then it would respond to Mod4+A instead.
TLDR Either Linux Mint MATE's Keyboard Shortcuts is completly bugged, or the support for (wired) Apple Aluminium Keyboard is very poor. I tend to think the latter because selecting "Apple Aluminium Keyboard (ANSI)" as keyboard model shows an error dialog about "XKB configuration".. I'm using "Apple Laptop" instead.
But the thing is, the key mapping just works fine. For example I can press Alt+Shift+L just like on a Mac to get the pipe character |, and basically all characters displayed on my keyboard function in a text editor. It's not a keyboard layout problem as such, it's the underlying support for modifier keys and keyboard shortcuts that doesn't play well with it.