Even when I'm not using 2 monitors, I use BandVMW (supplied in Object Desktop) and DesktopX seems not to be able to keep itself on all virtual desktops.
I tried the "Locked Windows" configuration of BandVMW bu DesktopX doesn't appear in the list of available windows to lock.
I'm able to get most objects work on the second monitor with the current beta of DX. The spider object even walks over there, but the fish stay away. I have a laptop, so I just keep a clock and date over there for when I have the second monitor plugged in, and DX is able to show it -- and leave it off of the screen when the second monitor is not being used (which is a change from previous versions). This was pretty much number one on my wish list - so I hope it gets to the point that it works with all vid cards.