I've been thinking about the widgets on desktop problem myself over the days since I saw the first videos, and in my mind have come to similar solutions as ragnar and elimoon8. That is, the user could move widgets to separate positions on portrait and landscape mode, and those positions would be remembered once set.

I propose that resizable widgets should allow the user to resize them separately in the two orientations (so if I resized it in one orientation, it would not affect the other orientation). That way you could have a one-line very wide widget in landscape mode that the user could chose to resize to a less wide two-line widget in portrait.

There might be a problem with non-resizable widgets which are wider in landscape mode than 480px. Maybe it should be a style guideline that no widget can force a minimum width greater than 480px.

I would suggest by default when you first rotate, individual widgets rotate around a point that makes sense, probably their mid-point, rather than falling to the bottom of the screen or similar. Maybe the widgets could also auto-resize so that at least all four corners are reachable to allow resizing. That would create a good first estimation, but then the user could tweak their position and size to suit the new orientation. Just to repeat to make clear, the positions and sizes would be remembered per widget separately for portrait and landscape. There could be some fancy transition eye candy if desired between the two states, so that the eye doesn't lose sight of the widget one is interested in when rotating.

As ragnar says, it's probably best to keep widgets on the same page in both orientations. Otherwise you might be looking at, say, a scrolling RSS widget, change orientation then find it disappears because it's not present on that page in the other orientation. For the same reason, I don't think the user should be allowed to hide widgets in one orientation vs the other, even if they cannot find an optimum position for the widget in both orientations, as that would later cause confusion, I'm sure.

Regarding the desktop wallpaper, I think by default just use the same wallpaper, but allow the user to use different wallpapers for the two orientations if they wish. That way, if they had text on a wallpaper (which would normally appear sideways on the other orientation), the user could choose different wallpaper that made sense in the other orientation.

In my mind, I think I would prefer to still swipe left and right to reach different pages in portrait mode (rather than up and down as suggested above), although without actually trying with a device I'm not 100% sure.