I have an installtion of Kubuntu 8.10 with KDE 4.1.2. I removed the panel and instead arranged most of the widgets on the desktop, inlcuding system tray. Now, the widget keeps being blank. Sounds a bit like http://bugs.kde.org/show_bug.cgi?id=168007, though this one is fixed since 4.1.0. My girlfriend experiences the same behaviour Hardy Heron (4.1.2 as well).

Any idea how to solve this?

ATM some of the widgets only seem to work on the panel or vice versa. Running the systray on the panel works, but adding another one on the desktop shows only a blank circle.
So i would assume that some widgets are only programmed for a specific containment.

Due to the current limitations of the systray spec the icons can only show up in one systray since the icons are, in fact, tiny embedded windows.

Dunno if the systray refactor in KDE 4.2 addresses this or not, but I think it might.

Actually, there is just one systray, but a new one, since the "original" has been removed together with the panel.

I noticed the same problem. When I add the systray widget to the plain screen, it starts as a tiny black circle(a rounded rectangle with minimal sides I would guess) and gets populated after a few seconds. This works fine as long as you don't move or resize it. In this case the frame moves as it is supposed to but the -- as jon sais -- windows move about twice the distance.
(And of course a restart of plasma leaves the tray box in the exact place where I left it and the same size, but without icons. Perhaps they are somewhere stranded in negative screen coordinates...)
I hope this helps the people who actually fix such things