If I tell Linux Mint to recognize two monitors by unchecking "same image on all monitors" and then try to set different resolution on each monitor then the desktop icons and panel vanish on the external, attached ADI monitor but not on the notebook monitor of my Acer Aspire One. I was able to set different resolutions on Ubuntu 12.04 on the same computer and same external monitor with the attached ADI monitor at 1024x768.

wassup with this?

I just tried setting both monitors to 800x600 --same thing happens: icons and panel disappear on the external monitor?

First of all, i'm not an expert on this..
Even though you have two monitors, there's only one desktop, spread across the two monitors. I'm guessing the external monitor is to the right of the notebook (at least in configuration). If you configure the external monitor to the left of the notebook, your icons will probably show up on the external display, with the panel still on the notebook. If you display the same image on both monitors, well, then you'll have the same image on both, but then of course you can't have different resolutions. I have a dual monitor setup (one monitor and one flat screen tv), however i have Nvidia graphics and can configure the two as separate X-screens in the Nvidia configuration tool. I'm then able to have individual panels and icons on each screen, with the disadvantage of not being able to move windows between screens. I have tried to configure a dual-screen setup on a computer without Nvidia graphics as separate X-screens without any luck..