Sorry for resurrecting an old thread but I had this exact same problem on my iPhone and I found a solution. There's an Accessibility Mode option in the latest version of WordPress (3.1.2 as of writing). I'm not sure when this appeared, but it certainly gets around the widget drag and drop issues on the touch screen devices.
On the Widgets page, go to Screen Options in the top right, choose Enable Accessibility Mode.
This gets rid of the drag and drop method, and adding widgets becomes a case of simply clicking on Add, and choosing the widget area you want it to go into with another click.
Sadly it's not implemented on the Custom Menus page (yet?) but it's a start.
I'm hoping that the upcoming 3.2 version will accommodate touch screen devices, as they're making a lot of changes to the admin panel. Fingers crossed.