I have a problem when I am creating Menus just for Mobile.

I Copied the menu menu to its own Mobile Menu and I placed it on the mj_all_header module position. It was showing up on the Mobile version with the menu selected items.

I have a problem that even though, the main menu on the desktop template has module positions set for different boxes (Such as an advertising box) for a given menu button, it will not show up unless I have also set the same menu item for the Mobile Menu. It seems that the Mobile Menu items overrides the Desktop Menu Items for displaying or not displaying on the desktop template.

Is there a way around this so the Mobile Menu does not interfere with other menus for displaying or not displaying boxes in different module positions?

My version of Joomla is 1.5.26 and the Mobile Joomla version is 1.1.0

Most likely you didn't change item aliases after copying. Actually, instead of create copies of menu items it's better to create aliases to them ("Alias" at the bottom of menu types list).