I can't change the secondary desktop wallpaper. I've already gone to system preferences and have chosen a wallpaper for second desktop, but it remains all white???
On Mountain Lion, you have to open System preferences and drag the window to corresponding desktop at which you want to change the wallpaper. Then select background picture of choice.
I occasionally use two monitors, and I use a program called SwitchResX (in the menu bar) to easily switch between resolutions, color spaces and monitor sets so I don't have to go to the clumsy system preference pane to click all over the place.
I have some scripts which automatically change desktop wallpapers. What I've noticed is that, you should basically have the monitor in question at least temporarily set as the main display when you want to change the wallpaper. When you're done choosing a wallpaper for it, you can set the other one as the main one again. Now the secondary monitor should keep the wallpaper that you've set. I believe this is a setting thing, but in my case I keep separate wallpapers on each monitor, and the time-specific scripts only affect my main monitor while the secondary one's wallpaper has to be changed manually, using the procedure that I just described.
I think you should be able to control wallpapers of multiple monitors using Mac's own system preferences, but since I found it so clumsy and don't do it that way, I can't assist more than what someone already said about it in the previous comment.