I noticed that the pressure of the rear wiper arm against the window is quite strong when you hold it a centimetre away from the glass, but weak when it's resting against the glass.
1. Removed the plastic bolt cap, cleaned out some dirt and sprayed the hinges with WD40. Tried the wiper and it worked properly!
2. Replaced the bolt cap. Tried the wiper and it had gone back to leaving a great big oval bit in the middle of the screen.
3. The bolt cap itself seems to be the problem. It needs a little judicious trimming / filing, because it gets in the way of the end bits of the arm and stops the arm having enough pressure against the window.
4. Filed a little off in several places where the bolt cap got in the way of the arm. Eventually this solved the problem. (I imagine the cleaning and the WD40 helped a bit, too.)