Maybe it was something I did wrong in my testing of LMDE 201204, but I couldn't find a way to adjust the set of system icons that showed up on my MATE desktop, i.e. the Computer, Home, Trash, Network icons. In normal Mint, there's a mintDesktop tool which provides a "Desktop Settings" panel for controlling the system desktop icons, and I think dconf-editor does it in gnome 3.
Eventually, I discovered that MATE has a MateConf Editor tool that provides easy MATE settings database editing capabilities. It can be downloaded via "apt-get install mate-conf-editor," and can be launched by typing "mateconf-editor" on the command line. It also shows up in MATE's menu as "Configuration Editor" after installation, with a red icon and description of "Directly edit your configuration database."
Using MateConf Editor, you can enable/disable the desktop icons by navigating to apps > caja > desktop.
Perhaps the pkg mate-conf-editor should be added to the standard MATE iso? Or is there a better alternative?
p.s. you can find my just-published review of MATE 201204 at http://deviceguru.com/my-week-with-debian