3.2 update can't click on interactive parts of admin frame

After updating to 3.2, I noticed I cannot upload images. The buttons to add images simply do not work – sometimes they open the flash uploader in a new tab, but this only happens once.

I also cannot select the main text field. Then I noticed that I couldn’t change the date published.

On other pages I do not seem to be able to click on drop-down boxes or text boxes. Radio buttons seem ok.

I moved all the plugins to a plugins.hold folder, and I changed the theme to 2010 but this did not help. I initially tried using a number of different browsers, but this did not help either.

I have backups for my site, so I assume I can re-install and start again. Could something have got screwed up during the automatic upgrade?